Daily Papers

Recent advancements in Latent Diffusion Models (LDMs) have revolutionized image synthesis and manipulation, raising significant concerns about data misappropriation and intellectual property infringement. While adversarial attacks have been extensively explored as a protective measure against such misuse of generative AI, current approaches are severely limited by their heavy reliance on model-specific knowledge and substantial computational costs. Drawing inspiration from the posterior collapse phenomenon observed in VAE training, we propose the Posterior Collapse Attack (PCA), a novel framework for protecting images from unauthorized manipulation. Through comprehensive theoretical analysis and empirical validation, we identify two distinct collapse phenomena during VAE inference: diffusion collapse and concentration collapse. Based on this discovery, we design a unified loss function that can flexibly achieve both types of collapse through parameter adjustment, each corresponding to different protection objectives in preventing image manipulation. Our method significantly reduces dependence on model-specific knowledge by requiring access to only the VAE encoder, which constitutes less than 4\% of LDM parameters. Notably, PCA achieves prompt-invariant protection by operating on the VAE encoder before text conditioning occurs, eliminating the need for empty prompt optimization required by existing methods. This minimal requirement enables PCA to maintain adequate transferability across various VAE-based LDM architectures while effectively preventing unauthorized image editing. Extensive experiments show PCA outperforms existing techniques in protection effectiveness, computational efficiency (runtime and VRAM), and generalization across VAE-based LDM variants. Our code is available at https://github.com/ZhongliangGuo/PosteriorCollapseAttack.

Conditional diffusion inversion provides a powerful framework for unpaired image-to-image translation. However, we demonstrate through an extensive analysis that standard deterministic inversion (e.g. DDIM) fails when the source domain is spectrally sparse compared to the target domain (e.g., super-resolution, sketch-to-image). In these contexts, the recovered latent from the input does not follow the expected isotropic Gaussian distribution. Instead it exhibits a signal with lower frequencies, locking target sampling to oversmoothed and texture-poor generations. We term this phenomenon spectral collapse. We observe that stochastic alternatives attempting to restore the noise variance tend to break the semantic link to the input, leading to structural drift. To resolve this structure-texture trade-off, we propose Orthogonal Variance Guidance (OVG), an inference-time method that corrects the ODE dynamics to enforce the theoretical Gaussian noise magnitude within the null-space of the structural gradient. Extensive experiments on microscopy super-resolution (BBBC021) and sketch-to-image (Edges2Shoes) demonstrate that OVG effectively restores photorealistic textures while preserving structural fidelity.

Fine-tuning foundation models via reinforcement learning (RL) has proven promising for aligning to downstream objectives. In the case of diffusion models (DMs), though RL training improves alignment from early timesteps, critical issues such as training instability and mode collapse arise. We address these drawbacks by exploiting the hierarchical nature of DMs: we train them dynamically at each epoch with a tailored RL method, allowing for continual evaluation and step-by-step refinement of the model performance (or alignment). Furthermore, we find that not every denoising step needs to be fine-tuned to align DMs to downstream tasks. Consequently, in addition to clipping, we regularise model parameters at distinct learning phases via a sliding-window approach. Our approach, termed Hierarchical Reward Fine-tuning (HRF), is validated on the Denoising Diffusion Policy Optimisation method, where we show that models trained with HRF achieve better preservation of diversity in downstream tasks, thus enhancing the fine-tuning robustness and at uncompromising mean rewards.

In this paper, we focus on the often-overlooked issue of embedding collapse in existing diffusion-based sequential recommendation models and propose ADRec, an innovative framework designed to mitigate this problem. Diverging from previous diffusion-based methods, ADRec applies an independent noise process to each token and performs diffusion across the entire target sequence during training. ADRec captures token interdependency through auto-regression while modeling per-token distributions through token-level diffusion. This dual approach enables the model to effectively capture both sequence dynamics and item representations, overcoming the limitations of existing methods. To further mitigate embedding collapse, we propose a three-stage training strategy: (1) pre-training the embedding weights, (2) aligning these weights with the ADRec backbone, and (3) fine-tuning the model. During inference, ADRec applies the denoising process only to the last token, ensuring that the meaningful patterns in historical interactions are preserved. Our comprehensive empirical evaluation across six datasets underscores the effectiveness of ADRec in enhancing both the accuracy and efficiency of diffusion-based sequential recommendation systems.

Training-free image editing with large diffusion models has become practical, yet faithfully performing complex non-rigid edits (e.g., pose or shape changes) remains highly challenging. We identify a key underlying cause: attention collapse in existing attention sharing mechanisms, where either positional embeddings or semantic features dominate visual content retrieval, leading to over-editing or under-editing. To address this issue, we introduce SynPS, a method that Synergistically leverages Positional embeddings and Semantic information for faithful non-rigid image editing. We first propose an editing measurement that quantifies the required editing magnitude at each denoising step. Based on this measurement, we design an attention synergy pipeline that dynamically modulates the influence of positional embeddings, enabling SynPS to balance semantic modifications and fidelity preservation. By adaptively integrating positional and semantic cues, SynPS effectively avoids both over- and under-editing. Extensive experiments on public and newly curated benchmarks demonstrate the superior performance and faithfulness of our approach.

Text-to-image (T2I) generative models achieve impressive visual fidelity but inherit and amplify demographic imbalances and cultural biases embedded in training data. We introduce T2I-BiasBench, a unified evaluation framework of thirteen complementary metrics that jointly captures demographic bias, element omission, and cultural collapse in diffusion models - the first framework to address all three dimensions simultaneously. We evaluate three open-source models - Stable Diffusion v1.5, BK-SDM Base, and Koala Lightning - against Gemini 2.5 Flash (RLHF-aligned) as a reference baseline. The benchmark comprises 1,574 generated images across five structured prompt categories. T2I-BiasBench integrates six established metrics with seven additional measures: four newly proposed (Composite Bias Score, Grounded Missing Rate, Implicit Element Missing Rate, Cultural Accuracy Ratio) and three adapted (Hallucination Score, Vendi Score, CLIP Proxy Score). Three key findings emerge: (1) Stable Diffusion v1.5 and BK-SDM exhibit bias amplification (>1.0) in beauty-related prompts; (2) contextual constraints such as surgical PPE substantially attenuate professional-role gender bias (Doctor CBS = 0.06 for SD v1.5); and (3) all models, including RLHF-aligned Gemini, collapse to a narrow set of cultural representations (CAS: 0.54-1.00), confirming that alignment techniques do not resolve cultural coverage gaps. T2I-BiasBench is publicly released to support standardized, fine-grained bias evaluation of generative models. The project page is available at: https://gyanendrachaubey.github.io/T2I-BiasBench/

Inference-time steering enables pretrained diffusion/flow models to be adapted to new tasks without retraining. A widely used approach is the ratio-of-densities method, which defines a time-indexed target path by reweighting probability-density trajectories from multiple models with positive, or in some cases, negative exponents. This construction, however, harbors a critical and previously unformalized failure mode: Marginal Path Collapse, where intermediate densities become non-normalizable even though endpoints remain valid. Collapse arises systematically when composing heterogeneous models trained on different noise schedules or datasets, including a common setting in molecular design where de-novo, conformer, and pocket-conditioned models must be combined for tasks such as flexible-pose scaffold decoration. We provide a novel and complete solution for the problem. First, we derive a simple path existence criterion that predicts exactly when collapse occurs from noise schedules and exponents alone. Second, we introduce Adaptive path Correction with Exponents (ACE), which extends Feynman-Kac steering to time-varying exponents and guarantees a valid probability path. On a synthetic 2D benchmark and on flexible-pose scaffold decoration, ACE eliminates collapse and enables high-guidance compositional generation, improving distributional and docking metrics over constant-exponent baselines and even specialized task-specific scaffold decoration models. Our work turns ratio-of-densities steering with heterogeneous experts from an unstable heuristic into a reliable tool for controllable generation.

Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the linear operator. In this paper, we propose GibbsDDRM, an extension of Denoising Diffusion Restoration Models (DDRM) to a blind setting in which the linear measurement operator is unknown. GibbsDDRM constructs a joint distribution of the data, measurements, and linear operator by using a pre-trained diffusion model for the data prior, and it solves the problem by posterior sampling with an efficient variant of a Gibbs sampler. The proposed method is problem-agnostic, meaning that a pre-trained diffusion model can be applied to various inverse problems without fine-tuning. In experiments, it achieved high performance on both blind image deblurring and vocal dereverberation tasks, despite the use of simple generic priors for the underlying linear operators.

Recent studies have demonstrated significant progress in aligning text-to-image diffusion models with human preference via Reinforcement Learning from Human Feedback. However, while existing methods achieve high scores on automated reward metrics, they often lead to Preference Mode Collapse (PMC)-a specific form of reward hacking where models converge on narrow, high-scoring outputs (e.g., images with monolithic styles or pervasive overexposure), severely degrading generative diversity. In this work, we introduce and quantify this phenomenon, proposing DivGenBench, a novel benchmark designed to measure the extent of PMC. We posit that this collapse is driven by over-optimization along the reward model's inherent biases. Building on this analysis, we propose Directional Decoupling Alignment (D^2-Align), a novel framework that mitigates PMC by directionally correcting the reward signal. Specifically, our method first learns a directional correction within the reward model's embedding space while keeping the model frozen. This correction is then applied to the reward signal during the optimization process, preventing the model from collapsing into specific modes and thereby maintaining diversity. Our comprehensive evaluation, combining qualitative analysis with quantitative metrics for both quality and diversity, reveals that D^2-Align achieves superior alignment with human preference.

Contemporary text-to-image models exhibit a surprising degree of mode collapse, as can be seen when sampling several images given the same text prompt. While previous work has attempted to address this issue by steering the model using guidance mechanisms, or by generating a large pool of candidates and refining them, in this work we take a different direction and aim for diversity in generations via noise optimization. Specifically, we show that a simple noise optimization objective can mitigate mode collapse while preserving the fidelity of the base model. We also analyze the frequency characteristics of the noise and show that alternative noise initializations with different frequency profiles can improve both optimization and search. Our experiments demonstrate that noise optimization yields superior results in terms of generation quality and variety.

Fine-tuning diffusion models via online reinforcement learning (RL) has shown great potential for enhancing text-to-image alignment. However, since precisely specifying a ground-truth objective for visual tasks remains challenging, the models are often optimized using a proxy reward that only partially captures the true goal. This mismatch often leads to reward hacking, where proxy scores increase while real image quality deteriorates and generation diversity collapses. While common solutions add regularization against the reference policy to prevent reward hacking, they compromise sample efficiency and impede the exploration of novel, high-reward regions, as the reference policy is usually sub-optimal. To address the competing demands of sample efficiency, effective exploration, and mitigation of reward hacking, we propose Gated and Adaptive Regularization with Diversity-aware Optimization (GARDO), a versatile framework compatible with various RL algorithms. Our key insight is that regularization need not be applied universally; instead, it is highly effective to selectively penalize a subset of samples that exhibit high uncertainty. To address the exploration challenge, GARDO introduces an adaptive regularization mechanism wherein the reference model is periodically updated to match the capabilities of the online policy, ensuring a relevant regularization target. To address the mode collapse issue in RL, GARDO amplifies the rewards for high-quality samples that also exhibit high diversity, encouraging mode coverage without destabilizing the optimization process. Extensive experiments across diverse proxy rewards and hold-out unseen metrics consistently show that GARDO mitigates reward hacking and enhances generation diversity without sacrificing sample efficiency or exploration, highlighting its effectiveness and robustness.

Existing feed-forward image-to-3D methods mainly rely on 2D multi-view diffusion models that cannot guarantee 3D consistency. These methods easily collapse when changing the prompt view direction and mainly handle object-centric prompt images. In this paper, we propose a novel single-stage 3D diffusion model, DiffusionGS, for object and scene generation from a single view. DiffusionGS directly outputs 3D Gaussian point clouds at each timestep to enforce view consistency and allow the model to generate robustly given prompt views of any directions, beyond object-centric inputs. Plus, to improve the capability and generalization ability of DiffusionGS, we scale up 3D training data by developing a scene-object mixed training strategy. Experiments show that our method enjoys better generation quality (2.20 dB higher in PSNR and 23.25 lower in FID) and over 5x faster speed (~6s on an A100 GPU) than SOTA methods. The user study and text-to-3D applications also reveals the practical values of our method. Our Project page at https://caiyuanhao1998.github.io/project/DiffusionGS/ shows the video and interactive generation results.

We introduce SceneDiffuser, a conditional generative model for 3D scene understanding. SceneDiffuser provides a unified model for solving scene-conditioned generation, optimization, and planning. In contrast to prior works, SceneDiffuser is intrinsically scene-aware, physics-based, and goal-oriented. With an iterative sampling strategy, SceneDiffuser jointly formulates the scene-aware generation, physics-based optimization, and goal-oriented planning via a diffusion-based denoising process in a fully differentiable fashion. Such a design alleviates the discrepancies among different modules and the posterior collapse of previous scene-conditioned generative models. We evaluate SceneDiffuser with various 3D scene understanding tasks, including human pose and motion generation, dexterous grasp generation, path planning for 3D navigation, and motion planning for robot arms. The results show significant improvements compared with previous models, demonstrating the tremendous potential of SceneDiffuser for the broad community of 3D scene understanding.

Synthesizing consistent and coherent long video remains a fundamental challenge. Existing methods suffer from semantic drift and narrative collapse over long horizons. We present A^2RD, an Agentic Auto-Regressive Diffusion architecture that decouples creative synthesis from consistency enforcement. A^2RD formulates long video synthesis as a closed-loop process that synthesizes and self-improves video segment-by-segment through a Retrieve--Synthesize--Refine--Update cycle. It comprises three core components: (i) Multimodal Video Memory that tracks video progression across modalities; (ii) Adaptive Segment Generation that switches among generation modes for natural progression and visual consistency; and (iii) Hierarchical Test-Time Self-Improvement that self-improves each segment at frame and video levels to prevent error propagation. We further introduce LVBench-C, a challenging benchmark with non-linear entity and environment transitions to stress-test long-horizon consistency. Across public and LVBench-C benchmarks spanning one- to ten-minute videos, A^2RD outperforms state-of-the-art baselines by up to 30% in consistency and 20% in narrative coherence. Human evaluations corroborate these gains while also highlighting notable improvements in motion and transition smoothness.

It is currently difficult to distill discrete diffusion models. In contrast, continuous diffusion literature has many distillation approaches methods that can reduce sampling steps to a handful. Our method, Discrete Moment Matching Distillation (D-MMD), leverages ideas that have been highly successful in the continuous domain. Whereas previous discrete distillation methods collapse, D-MMD maintains high quality and diversity (given sufficient sampling steps). This is demonstrated on both text and image datasets. Moreover, the newly distilled generators can outperform their teachers.

World models aim to predict plausible futures consistent with past observations, a capability central to planning and decision-making in reinforcement learning. Yet, existing architectures face a fundamental memory trade-off: transformers preserve local detail but are bottlenecked by quadratic attention, while recurrent and state-space models scale more efficiently but compress history at the cost of fidelity. To overcome this trade-off, we suggest decoupling future-past consistency from any single architecture and instead leveraging a set of specialized experts. We introduce a diffusion-based framework that integrates heterogeneous memory models through a contrastive product-of-experts formulation. Our approach instantiates three complementary roles: a short-term memory expert that captures fine local dynamics, a long-term memory expert that stores episodic history in external diffusion weights via lightweight test-time finetuning, and a spatial long-term memory expert that enforces geometric and spatial coherence. This compositional design avoids mode collapse and scales to long contexts without incurring a quadratic cost. Across simulated and real-world benchmarks, our method improves temporal consistency, recall of past observations, and navigation performance, establishing a novel paradigm for building and operating memory-augmented diffusion world models.

Scaling Diffusion Transformers (DiTs) to hundreds of layers introduces a structural vulnerability: networks can enter a silent, mean-dominated collapse state that homogenizes token representations and suppresses centered variation. Through mechanistic auditing, we isolate the trigger event of this collapse as Mean Mode Screaming (MMS). MMS can occur even when training appears stable, with a mean-coherent backward shock on residual writers that opens deep residual branches and drives the network into a mean-dominated state. We show this behavior is driven by an exact decomposition of these gradients into mean-coherent and centered components, compounded by the structural suppression of attention-logit gradients through the null space of the Softmax Jacobian once values homogenize. To address this, we propose Mean-Variance Split (MV-Split) Residuals, which combine a separately gained centered residual update with a leaky trunk-mean replacement. On a 400-layer single-stream DiT, MV-Split prevents the divergent collapse that crashes the un-stabilized baseline; it tracks close to the baseline's pre-crash trajectory while remaining substantially better than token-isotropic gating methods such as LayerScale across the full schedule. Finally, we present a 1000-layer DiT as a scale-validation run at boundary scales, establishing that the architecture remains stably trainable at extreme depth.

Score distillation sampling has been pivotal for integrating diffusion models into generation of complex visuals. Despite impressive results it suffers from mode collapse and lack of diversity. To cope with this challenge, we leverage the gradient flow interpretation of score distillation to propose Repulsive Score Distillation (RSD). In particular, we propose a variational framework based on repulsion of an ensemble of particles that promotes diversity. Using a variational approximation that incorporates a coupling among particles, the repulsion appears as a simple regularization that allows interaction of particles based on their relative pairwise similarity, measured e.g., via radial basis kernels. We design RSD for both unconstrained and constrained sampling scenarios. For constrained sampling we focus on inverse problems in the latent space that leads to an augmented variational formulation, that strikes a good balance between compute, quality and diversity. Our extensive experiments for text-to-image generation, and inverse problems demonstrate that RSD achieves a superior trade-off between diversity and quality compared with state-of-the-art alternatives.

Generative Artificial Intelligence image models have achieved outstanding performance in text-to-image generation and other tasks, such as inpainting that completes images with missing fragments. The performance of inpainting can be accurately measured by taking an image, removing some fragments, performing the inpainting to restore them, and comparing the results with the original image. Interestingly, inpainting can also be applied recursively, starting from an image, removing some parts, applying inpainting to reconstruct the image, and then starting the inpainting process again on the reconstructed image, and so forth. This process of recursively applying inpainting can lead to an image that is similar or completely different from the original one, depending on the fragments that are removed and the ability of the model to reconstruct them. Intuitively, stability, understood as the capability to recover an image that is similar to the original one even after many recursive inpainting operations, is a desirable feature and can be used as an additional performance metric for inpainting. The concept of stability is also being studied in the context of recursive training of generative AI models with their own data. Recursive inpainting is an inference-only recursive process whose understanding may complement ongoing efforts to study the behavior of generative AI models under training recursion. In this paper, the impact of recursive inpainting is studied for one of the most widely used image models: Stable Diffusion. The results show that recursive inpainting can lead to image collapse, so ending with a nonmeaningful image, and that the outcome depends on several factors such as the type of image, the size of the inpainting masks, and the number of iterations.

Video generation has recently emerged as a central task in the field of generative AI. However, the substantial computational cost inherent in video synthesis makes model distillation a critical technique for efficient deployment. Despite its significance, there is a scarcity of methods specifically designed for video diffusion models. Prevailing approaches often directly adapt image distillation techniques, which frequently lead to artifacts such as oversaturation, temporal inconsistency, and mode collapse. To address these challenges, we propose a novel distillation framework tailored specifically for video diffusion models. Its core innovations include: (1) an adaptive regression loss that dynamically adjusts spatial supervision weights to prevent artifacts arising from excessive distribution shifts; (2) a temporal regularization loss to counteract temporal collapse, promoting smooth and physically plausible sampling trajectories; and (3) an inference-time frame interpolation strategy that reduces sampling overhead while preserving perceptual quality. Extensive experiments and ablation studies on the VBench and VBench2 benchmarks demonstrate that our method achieves stable few-step video synthesis, significantly enhancing perceptual fidelity and motion realism. It consistently outperforms existing distillation baselines across multiple metrics.

Traditional video codecs optimized for pixel fidelity collapse at ultra-low bitrates and produce severe artifacts. This failure arises from a fundamental misalignment between pixel accuracy and human perception. We propose a semantic video compression framework named DiSCo that transmits only the most meaningful information while relying on generative priors for detail synthesis. The source video is decomposed into three compact modalities: a textual description, a spatiotemporally degraded video, and optional sketches or poses that respectively capture semantic, appearance, and motion cues. A conditional video diffusion model then reconstructs high-quality, temporally coherent videos from these compact representations. Temporal forward filling, token interleaving, and modality-specific codecs are proposed to improve multimodal generation and modality compactness. Experiments show that our method outperforms baseline semantic and traditional codecs by 2-10X on perceptual metrics at low bitrates.

The proliferation of generative models, combined with pretraining on web-scale data, raises a timely question: what happens when these models are trained on their own generated outputs? Recent investigations into model-data feedback loops proposed that such loops would lead to a phenomenon termed model collapse, under which performance progressively degrades with each model-data feedback iteration until fitted models become useless. However, those studies largely assumed that new data replace old data over time, where an arguably more realistic assumption is that data accumulate over time. In this paper, we ask: what effect does accumulating data have on model collapse? We empirically study this question by pretraining sequences of language models on text corpora. We confirm that replacing the original real data by each generation's synthetic data does indeed tend towards model collapse, then demonstrate that accumulating the successive generations of synthetic data alongside the original real data avoids model collapse; these results hold across a range of model sizes, architectures, and hyperparameters. We obtain similar results for deep generative models on other types of real data: diffusion models for molecule conformation generation and variational autoencoders for image generation. To understand why accumulating data can avoid model collapse, we use an analytically tractable framework introduced by prior work in which a sequence of linear models are fit to the previous models' outputs. Previous work used this framework to show that if data are replaced, the test error increases with the number of model-fitting iterations; we extend this argument to prove that if data instead accumulate, the test error has a finite upper bound independent of the number of iterations, meaning model collapse no longer occurs.

Negative guidance -- explicitly suppressing unwanted attributes -- remains a fundamental challenge in diffusion models, particularly in few-step sampling regimes. While Classifier-Free Guidance (CFG) works well in standard settings, it fails under aggressive sampling step compression due to divergent predictions between positive and negative branches. We present Normalized Attention Guidance (NAG), an efficient, training-free mechanism that applies extrapolation in attention space with L1-based normalization and refinement. NAG restores effective negative guidance where CFG collapses while maintaining fidelity. Unlike existing approaches, NAG generalizes across architectures (UNet, DiT), sampling regimes (few-step, multi-step), and modalities (image, video), functioning as a universal plug-in with minimal computational overhead. Through extensive experimentation, we demonstrate consistent improvements in text alignment (CLIP Score), fidelity (FID, PFID), and human-perceived quality (ImageReward). Our ablation studies validate each design component, while user studies confirm significant preference for NAG-guided outputs. As a model-agnostic inference-time approach requiring no retraining, NAG provides effortless negative guidance for all modern diffusion frameworks -- pseudocode in the Appendix!

Text-to-image diffusion models achieve impressive visual fidelity, yet they remain unreliable in multi-object generation. Despite extensive empirical evidence of these failures, the underlying causes remain unclear. We begin by asking how much of this limitation arises from the data itself. To disentangle data effects, we consider two regimes across different dataset sizes: (1) concept generalization, where each individual concept is observed during training under potentially imbalanced data distributions, and (2) compositional generalization, where specific combinations of concepts are systematically held out. To study these regimes, we introduce mosaic (Multi-Object Spatial relations, AttrIbution, Counting), a controlled framework for dataset generation. By training diffusion models on mosaic, we find that scene complexity plays a dominant role rather than concept imbalance, and that counting is uniquely difficult to learn in low-data regimes. Moreover, compositional generalization collapses as more concept combinations are held out during training. These findings highlight fundamental limitations of diffusion models and motivate stronger inductive biases and data design for robust multi-object compositional generation.

Diffusion and flow models achieve State-Of-The-Art (SOTA) generative performance, yet many practically important behaviors such as fine-grained prompt fidelity, compositional correctness, and text rendering are weakly specified by score or flow matching pretraining objectives. Reinforcement Learning (RL) fine-tuning with external, black-box rewards is a natural remedy, but diffusion RL is often brittle. Trajectory-based methods incur high memory cost and high-variance gradient estimates; forward-process approaches converge faster but can suffer from distribution drift, and hence reward hacking. In this work, we present Centered Reward Distillation (CRD), a diffusion RL framework derived from KL-regularized reward maximization built on forward-process-based fine-tuning. The key insight is that the intractable normalizing constant cancels under within-prompt centering, yielding a well-posed reward-matching objective. To enable reliable text-to-image fine-tuning, we introduce techniques that explicitly control distribution drift: (i) decoupling the sampler from the moving reference to prevent ratio-signal collapse, (ii) KL anchoring to a CFG-guided pretrained model to control long-run drift and align with the inference-time semantics of the pre-trained model, and (iii) reward-adaptive KL strength to accelerate early learning under large KL regularization while reducing late-stage exploitation of reward-model loopholes. Experiments on text-to-image post-training with GenEval and OCR rewards show that CRD achieves competitive SOTA reward optimization results with fast convergence and reduced reward hacking, as validated on unseen preference metrics.

Human-level contact-rich manipulation relies on the distinct roles of two key modalities: vision provides spatially rich but temporally slow global context, while force sensing captures rapid, high-frequency local contact dynamics. Integrating these signals is challenging due to their fundamental frequency and informational disparities. In this work, we propose ImplicitRDP, a unified end-to-end visual-force diffusion policy that integrates visual planning and reactive force control within a single network. We introduce Structural Slow-Fast Learning, a mechanism utilizing causal attention to simultaneously process asynchronous visual and force tokens, allowing the policy to perform closed-loop adjustments at the force frequency while maintaining the temporal coherence of action chunks. Furthermore, to mitigate modality collapse where end-to-end models fail to adjust the weights across different modalities, we propose Virtual-target-based Representation Regularization. This auxiliary objective maps force feedback into the same space as the action, providing a stronger, physics-grounded learning signal than raw force prediction. Extensive experiments on contact-rich tasks demonstrate that ImplicitRDP significantly outperforms both vision-only and hierarchical baselines, achieving superior reactivity and success rates with a streamlined training pipeline. Code and videos will be publicly available at https://implicit-rdp.github.io.

Recent progress in multimodal large language models (MLLMs) has highlighted the challenge of efficiently bridging pre-trained Vision-Language Models (VLMs) with Diffusion Models. While methods using a fixed number of learnable query tokens offer computational efficiency, they suffer from task generalization collapse, failing to adapt to new tasks that are distant from their pre-training tasks. To overcome this, we propose Noisy Query Tokens, which learn a distributed representation space between the VLM and Diffusion Model via end-to-end optimization, enhancing continual learning. Additionally, we introduce a VAE branch with linear projection to recover fine-grained image details. Experimental results confirm our approach mitigates generalization collapse and enables stable continual learning across diverse tasks.

Deep image restoration models aim to learn a mapping from degraded image space to natural image space. However, they face several critical challenges: removing degradation, generating realistic details, and ensuring pixel-level consistency. Over time, three major classes of methods have emerged, including MSE-based, GAN-based, and diffusion-based methods. However, they fail to achieve a good balance between restoration quality, fidelity, and speed. We propose a novel method, HYPIR, to address these challenges. Our solution pipeline is straightforward: it involves initializing the image restoration model with a pre-trained diffusion model and then fine-tuning it with adversarial training. This approach does not rely on diffusion loss, iterative sampling, or additional adapters. We theoretically demonstrate that initializing adversarial training from a pre-trained diffusion model positions the initial restoration model very close to the natural image distribution. Consequently, this initialization improves numerical stability, avoids mode collapse, and substantially accelerates the convergence of adversarial training. Moreover, HYPIR inherits the capabilities of diffusion models with rich user control, enabling text-guided restoration and adjustable texture richness. Requiring only a single forward pass, it achieves faster convergence and inference speed than diffusion-based methods. Extensive experiments show that HYPIR outperforms previous state-of-the-art methods, achieving efficient and high-quality image restoration.

Recently, convolutional networks have achieved remarkable development in remote sensing image Super-Resoltuion (SR) by minimizing the regression objectives, e.g., MSE loss. However, despite achieving impressive performance, these methods often suffer from poor visual quality with over-smooth issues. Generative adversarial networks have the potential to infer intricate details, but they are easy to collapse, resulting in undesirable artifacts. To mitigate these issues, in this paper, we first introduce Diffusion Probabilistic Model (DPM) for efficient remote sensing image SR, dubbed EDiffSR. EDiffSR is easy to train and maintains the merits of DPM in generating perceptual-pleasant images. Specifically, different from previous works using heavy UNet for noise prediction, we develop an Efficient Activation Network (EANet) to achieve favorable noise prediction performance by simplified channel attention and simple gate operation, which dramatically reduces the computational budget. Moreover, to introduce more valuable prior knowledge into the proposed EDiffSR, a practical Conditional Prior Enhancement Module (CPEM) is developed to help extract an enriched condition. Unlike most DPM-based SR models that directly generate conditions by amplifying LR images, the proposed CPEM helps to retain more informative cues for accurate SR. Extensive experiments on four remote sensing datasets demonstrate that EDiffSR can restore visual-pleasant images on simulated and real-world remote sensing images, both quantitatively and qualitatively. The code of EDiffSR will be available at https://github.com/XY-boy/EDiffSR

Animating virtual avatars to make co-speech gestures facilitates various applications in human-machine interaction. The existing methods mainly rely on generative adversarial networks (GANs), which typically suffer from notorious mode collapse and unstable training, thus making it difficult to learn accurate audio-gesture joint distributions. In this work, we propose a novel diffusion-based framework, named Diffusion Co-Speech Gesture (DiffGesture), to effectively capture the cross-modal audio-to-gesture associations and preserve temporal coherence for high-fidelity audio-driven co-speech gesture generation. Specifically, we first establish the diffusion-conditional generation process on clips of skeleton sequences and audio to enable the whole framework. Then, a novel Diffusion Audio-Gesture Transformer is devised to better attend to the information from multiple modalities and model the long-term temporal dependency. Moreover, to eliminate temporal inconsistency, we propose an effective Diffusion Gesture Stabilizer with an annealed noise sampling strategy. Benefiting from the architectural advantages of diffusion models, we further incorporate implicit classifier-free guidance to trade off between diversity and gesture quality. Extensive experiments demonstrate that DiffGesture achieves state-of-theart performance, which renders coherent gestures with better mode coverage and stronger audio correlations. Code is available at https://github.com/Advocate99/DiffGesture.

Reinforcement Learning (RL) post-training has become the standard for aligning generative models with human preferences, yet most methods rely on a single scalar reward. When multiple criteria matter, the prevailing practice of ``early scalarization'' collapses rewards into a fixed weighted sum. This commits the model to a single trade-off point at training time, providing no inference-time control over inherently conflicting goals -- such as prompt adherence versus source fidelity in image editing. We introduce ParetoSlider, a multi-objective RL (MORL) framework that trains a single diffusion model to approximate the entire Pareto front. By training the model with continuously varying preference weights as a conditioning signal, we enable users to navigate optimal trade-offs at inference time without retraining or maintaining multiple checkpoints. We evaluate ParetoSlider across three state-of-the-art flow-matching backbones: SD3.5, FluxKontext, and LTX-2. Our single preference-conditioned model matches or exceeds the performance of baselines trained separately for fixed reward trade-offs, while uniquely providing fine-grained control over competing generative goals.

Recent advances in generative artificial intelligence, particularly large language models (LLMs), have opened new opportunities for enhancing recommender systems (RecSys). Most existing LLM-based RecSys approaches operate in a discrete space, using vector-quantized tokenizers to align with the inherent discrete nature of language models. However, these quantization methods often result in lossy tokenization and suboptimal learning, primarily due to inaccurate gradient propagation caused by the non-differentiable argmin operation in standard vector quantization. Inspired by the emerging trend of embracing continuous tokens in language models, we propose ContRec, a novel framework that seamlessly integrates continuous tokens into LLM-based RecSys. Specifically, ContRec consists of two key modules: a sigma-VAE Tokenizer, which encodes users/items with continuous tokens; and a Dispersive Diffusion module, which captures implicit user preference. The tokenizer is trained with a continuous Variational Auto-Encoder (VAE) objective, where three effective techniques are adopted to avoid representation collapse. By conditioning on the previously generated tokens of the LLM backbone during user modeling, the Dispersive Diffusion module performs a conditional diffusion process with a novel Dispersive Loss, enabling high-quality user preference generation through next-token diffusion. Finally, ContRec leverages both the textual reasoning output from the LLM and the latent representations produced by the diffusion model for Top-K item retrieval, thereby delivering comprehensive recommendation results. Extensive experiments on four datasets demonstrate that ContRec consistently outperforms both traditional and SOTA LLM-based recommender systems. Our results highlight the potential of continuous tokenization and generative modeling for advancing the next generation of recommender systems.

Hematoxylin and Eosin (H&E) staining is widely regarded as the standard in pathology for diagnosing diseases and tracking tumor recurrence. While H&E staining shows tissue structures, it lacks the ability to reveal specific proteins that are associated with disease severity and treatment response. Immunohistochemical (IHC) stains use antibodies to highlight the expression of these proteins on their respective cell types, improving diagnostic accuracy, and assisting with drug selection for treatment. Despite their value, IHC stains require additional time and resources, limiting their utilization in some clinical settings. Recent advances in deep learning have positioned Image-to-Image (I2I) translation as a computational, cost-effective alternative for IHC. I2I generates high fidelity stain transformations digitally, potentially replacing manual staining in IHC. Diffusion models, the current state of the art in image generation and conditional tasks, are particularly well suited for virtual IHC due to their ability to produce high quality images and resilience to mode collapse. However, these models require extensive and diverse datasets (often millions of samples) to achieve a robust performance, a challenge in virtual staining applications where only thousands of samples are typically available. Inspired by the success of multitask deep learning models in scenarios with limited data, we introduce STAINDIFFUSER, a novel multitask diffusion architecture tailored to virtual staining that achieves convergence with smaller datasets. STAINDIFFUSER simultaneously trains two diffusion processes: (a) generating cell specific IHC stains from H&E images and (b) performing H&E based cell segmentation, utilizing coarse segmentation labels exclusively during training. STAINDIFFUSER generates high-quality virtual stains for two markers, outperforming over twenty I2I baselines.

Diffusion Large Language Models (dLLMs) break the rigid left-to-right constraint of traditional LLMs, enabling token generation in arbitrary orders. Intuitively, this flexibility implies a solution space that strictly supersets the fixed autoregressive trajectory, theoretically unlocking superior reasoning potential for general tasks like mathematics and coding. Consequently, numerous works have leveraged reinforcement learning (RL) to elicit the reasoning capability of dLLMs. In this paper, we reveal a counter-intuitive reality: arbitrary order generation, in its current form, narrows rather than expands the reasoning boundary of dLLMs. We find that dLLMs tend to exploit this order flexibility to bypass high-uncertainty tokens that are crucial for exploration, leading to a premature collapse of the solution space. This observation challenges the premise of existing RL approaches for dLLMs, where considerable complexities, such as handling combinatorial trajectories and intractable likelihoods, are often devoted to preserving this flexibility. We demonstrate that effective reasoning is better elicited by intentionally forgoing arbitrary order and applying standard Group Relative Policy Optimization (GRPO) instead. Our approach, JustGRPO, is minimalist yet surprisingly effective (e.g., 89.1% accuracy on GSM8K) while fully retaining the parallel decoding ability of dLLMs. Project page: https://nzl-thu.github.io/the-flexibility-trap

Distilled diffusion models suffer from a critical limitation: reduced sample diversity compared to their base counterparts. In this work, we uncover that despite this diversity loss, distilled models retain the fundamental concept representations of base models. We demonstrate control distillation - where control mechanisms like Concept Sliders and LoRAs trained on base models can be seamlessly transferred to distilled models and vice-versa, effectively distilling control without any retraining. This preservation of representational structure prompted our investigation into the mechanisms of diversity collapse during distillation. To understand how distillation affects diversity, we introduce Diffusion Target (DT) Visualization, an analysis and debugging tool that reveals how models predict final outputs at intermediate steps. Through DT-Visualization, we identify generation artifacts, inconsistencies, and demonstrate that initial diffusion timesteps disproportionately determine output diversity, while later steps primarily refine details. Based on these insights, we introduce diversity distillation - a hybrid inference approach that strategically employs the base model for only the first critical timestep before transitioning to the efficient distilled model. Our experiments demonstrate that this simple modification not only restores the diversity capabilities from base to distilled models but surprisingly exceeds it, while maintaining nearly the computational efficiency of distilled inference, all without requiring additional training or model modifications. Our code and data are available at https://distillation.baulab.info

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

Earth observation applications increasingly rely on data from multiple sensors, including optical, radar, elevation, and land-cover. Relationships between modalities are fundamental for data integration but are inherently non-injective: identical conditioning information can correspond to multiple physically plausible observations, and should be parametrised as conditional distributions. Deterministic models, by contrast, collapse toward conditional means and fail to represent the uncertainty and variability required for tasks such as data completion and cross-sensor translation. We introduce COP-GEN, a multimodal latent diffusion transformer that models the joint distribution of heterogeneous EO modalities at their native spatial resolutions. By parameterising cross-modal mappings as conditional distributions, COP-GEN enables flexible any-to-any conditional generation, including zero-shot modality translation without task-specific retraining. Experiments show that COP-GEN generates diverse yet physically consistent realisations while maintaining strong peak fidelity across optical, radar, and elevation modalities. Qualitative and quantitative analyses demonstrate that the model captures meaningful cross-modal structure and adapts its output uncertainty as conditioning information increases. We release a stochastic benchmark built from multi-temporal Sentinel-2 observations that enables distribution-level comparison of generative EO models. On this benchmark, COP-GEN covers 90% of the real observation manifold and 63% of its per-band reflectance range, while the strongest competing method collapses to 2.8% and 18%, respectively. These results highlight the importance of stochastic generative modeling for EO and motivate evaluation protocols beyond single-reference, pointwise metrics. Website: https://miquel-espinosa.github.io/cop-gen

Latent diffusion models have emerged as the dominant framework for high-fidelity and efficient image generation, owing to their ability to learn diffusion processes in compact latent spaces. However, while previous research has focused primarily on reconstruction accuracy and semantic alignment of the latent space, we observe that another critical factor, robustness to sampling perturbations, also plays a crucial role in determining generation quality. Through empirical and theoretical analyses, we show that the commonly used β-VAE-based tokenizers in latent diffusion models, tend to produce overly compact latent manifolds that are highly sensitive to stochastic perturbations during diffusion sampling, leading to visual degradation. To address this issue, we propose a simple yet effective solution that constructs a latent space robust to sampling perturbations while maintaining strong reconstruction fidelity. This is achieved by introducing a Variance Expansion loss that counteracts variance collapse and leverages the adversarial interplay between reconstruction and variance expansion to achieve an adaptive balance that preserves reconstruction accuracy while improving robustness to stochastic sampling. Extensive experiments demonstrate that our approach consistently enhances generation quality across different latent diffusion architectures, confirming that robustness in latent space is a key missing ingredient for stable and faithful diffusion sampling.

Discrete diffusion models offer global context awareness and flexible parallel generation. However, uniform random noise schedulers in standard DLLM training overlook the highly non-uniform information density inherent in real-world sequences. This wastes optimization resources on low-density structural glues while leaving high-density logical pivot points severely under-optimized. To address this, we propose an Information Density Driven Smart Noise Scheduler. By extracting information-dense hubs and applying Complementary Priority Masking, our method decouples a single training instance into mutually reinforcing reasoning and syntax samples, forcing the model to master both logical deduction and foundational sequence structure. Experiments demonstrate that our approach improves average accuracy by ~4\% across four Code and Math reasoning benchmarks, significantly outperforming uniform baselines. Mechanistic analyses further reveal that probabilistic priority masking effectively mitigates contextual collapse during block diffusion training. Overall, this density-aware strategy efficiently unlocks the reasoning potential of diffusion language models at minimal annotation cost, emerging as a promising new masked data training paradigm for Diffusion LLMs. Our processed dataset can be found at https://huggingface.co/datasets/malr07/opc-sft-stage2-dense-extracted.

Leveraging pre-trained Diffusion Transformers (DiTs) for high-resolution (HR) image synthesis often leads to spatial layout collapse and degraded texture fidelity. Prior work mitigates these issues with complex pipelines that first perform a base-resolution (i.e., training-resolution) denoising process to guide HR generation. We instead explore the intrinsic generative mechanisms of DiTs and propose ResDiT, a training-free method that scales resolution efficiently. We identify the core factor governing spatial layout, position embeddings (PEs), and show that the original PEs encode incorrect positional information when extrapolated to HR, which triggers layout collapse. To address this, we introduce a PE scaling technique that rectifies positional encoding under resolution changes. To further remedy low-fidelity details, we develop a local-enhancement mechanism grounded in base-resolution local attention. We design a patch-level fusion module that aggregates global and local cues, together with a Gaussian-weighted splicing strategy that eliminates grid artifacts. Comprehensive evaluations demonstrate that ResDiT consistently delivers high-fidelity, high-resolution image synthesis and integrates seamlessly with downstream tasks, including spatially controlled generation.

Distribution Matching Distillation (DMD) is a promising score distillation technique that compresses pre-trained teacher diffusion models into efficient one-step or multi-step student generators. Nevertheless, its reliance on the reverse Kullback-Leibler (KL) divergence minimization potentially induces mode collapse (or mode-seeking) in certain applications. To circumvent this inherent drawback, we propose Adversarial Distribution Matching (ADM), a novel framework that leverages diffusion-based discriminators to align the latent predictions between real and fake score estimators for score distillation in an adversarial manner. In the context of extremely challenging one-step distillation, we further improve the pre-trained generator by adversarial distillation with hybrid discriminators in both latent and pixel spaces. Different from the mean squared error used in DMD2 pre-training, our method incorporates the distributional loss on ODE pairs collected from the teacher model, and thus providing a better initialization for score distillation fine-tuning in the next stage. By combining the adversarial distillation pre-training with ADM fine-tuning into a unified pipeline termed DMDX, our proposed method achieves superior one-step performance on SDXL compared to DMD2 while consuming less GPU time. Additional experiments that apply multi-step ADM distillation on SD3-Medium, SD3.5-Large, and CogVideoX set a new benchmark towards efficient image and video synthesis.

Currently, methods for single-image deblurring based on CNNs and transformers have demonstrated promising performance. However, these methods often suffer from perceptual limitations, poor generalization ability, and struggle with heavy or complex blur. While diffusion-based methods can partially address these shortcomings, their multi-step denoising process limits their practical usage. In this paper, we conduct an in-depth exploration of diffusion models in deblurring and propose a one-step diffusion model for deblurring (OSDD), a novel framework that reduces the denoising process to a single step, significantly improving inference efficiency while maintaining high fidelity. To tackle fidelity loss in diffusion models, we introduce an enhanced variational autoencoder (eVAE), which improves structural restoration. Additionally, we construct a high-quality synthetic deblurring dataset to mitigate perceptual collapse and design a dynamic dual-adapter (DDA) to enhance perceptual quality while preserving fidelity. Extensive experiments demonstrate that our method achieves strong performance on both full and no-reference metrics. Our code and pre-trained model will be publicly available at https://github.com/xyLiu339/OSDD.

Discrete diffusion models offer a promising alternative to autoregressive generation through parallel decoding, but they suffer from a sampling wall: once categorical sampling occurs, rich distributional information collapses into one-hot vectors and cannot be propagated across steps, forcing subsequent steps to operate with limited information. To mitigate this problem, we introduce Loopholing, a novel and simple mechanism that preserves this information via a deterministic latent pathway, leading to Loopholing Discrete Diffusion Models (LDDMs). Trained efficiently with a self-conditioning strategy, LDDMs achieve substantial gains-reducing generative perplexity by up to 61% over prior baselines, closing (and in some cases surpassing) the gap with autoregressive models, and producing more coherent text. Applied to reasoning tasks, LDDMs also improve performance on arithmetic benchmarks such as Countdown and Game of 24. These results also indicate that loopholing mitigates idle steps and oscillations, providing a scalable path toward high-quality non-autoregressive text generation.

Representation learning is all about discovering the hidden modular attributes that generate the data faithfully. We explore the potential of Denoising Diffusion Probabilistic Model (DM) in unsupervised learning of the modular attributes. We build a theoretical framework that connects the diffusion time-steps and the hidden attributes, which serves as an effective inductive bias for unsupervised learning. Specifically, the forward diffusion process incrementally adds Gaussian noise to samples at each time-step, which essentially collapses different samples into similar ones by losing attributes, e.g., fine-grained attributes such as texture are lost with less noise added (i.e., early time-steps), while coarse-grained ones such as shape are lost by adding more noise (i.e., late time-steps). To disentangle the modular attributes, at each time-step t, we learn a t-specific feature to compensate for the newly lost attribute, and the set of all 1,...,t-specific features, corresponding to the cumulative set of lost attributes, are trained to make up for the reconstruction error of a pre-trained DM at time-step t. On CelebA, FFHQ, and Bedroom datasets, the learned feature significantly improves attribute classification and enables faithful counterfactual generation, e.g., interpolating only one specified attribute between two images, validating the disentanglement quality. Codes are in https://github.com/yue-zhongqi/diti.

We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces geodesics to decode as straight segments in data space, effectively ignoring any intrinsic data geometry beyond the ambient Euclidean space. Complementing this view, diffusion also admits a stochastic decoder via the reverse SDE, which enables an information geometric treatment with the Fisher-Rao metric. However, a choice of x_T as the latent representation collapses this metric due to memorylessness. We address this by introducing a latent spacetime z=(x_t,t) that indexes the family of denoising distributions p(x_0 | x_t) across all noise scales, yielding a nontrivial geometric structure. We prove these distributions form an exponential family and derive simulation-free estimators for curve lengths, enabling efficient geodesic computation. The resulting structure induces a principled Diffusion Edit Distance, where geodesics trace minimal sequences of noise and denoise edits between data. We also demonstrate benefits for transition path sampling in molecular systems, including constrained variants such as low-variance transitions and region avoidance. Code is available at: https://github.com/rafalkarczewski/spacetime-geometry.

Multimodal generative models require a unified approach to handle both discrete data (e.g., text and code) and continuous data (e.g., image, audio, video). In this work, we propose Latent Language Modeling (LatentLM), which seamlessly integrates continuous and discrete data using causal Transformers. Specifically, we employ a variational autoencoder (VAE) to represent continuous data as latent vectors and introduce next-token diffusion for autoregressive generation of these vectors. Additionally, we develop sigma-VAE to address the challenges of variance collapse, which is crucial for autoregressive modeling. Extensive experiments demonstrate the effectiveness of LatentLM across various modalities. In image generation, LatentLM surpasses Diffusion Transformers in both performance and scalability. When integrated into multimodal large language models, LatentLM provides a general-purpose interface that unifies multimodal generation and understanding. Experimental results show that LatentLM achieves favorable performance compared to Transfusion and vector quantized models in the setting of scaling up training tokens. In text-to-speech synthesis, LatentLM outperforms the state-of-the-art VALL-E 2 model in speaker similarity and robustness, while requiring 10x fewer decoding steps. The results establish LatentLM as a highly effective and scalable approach to advance large multimodal models.

Efficiency, as a critical practical challenge for LLM-driven agentic and reasoning systems, is increasingly constrained by the inherent latency of autoregressive (AR) decoding. Speculative decoding mitigates this cost through a draft-verify scheme, yet existing approaches rely on AR draft models (a.k.a., drafters), which introduce two fundamental issues: (1) step-wise uncertainty accumulation leads to a progressive collapse of trust between the target model and the drafter, and (2) inherently sequential decoding of AR drafters. Together, these factors cause limited speedups. In this paper, we show that a diffusion large language model (dLLM) drafters can naturally overcome these issues through its fundamentally different probabilistic modeling and efficient parallel decoding strategy. Building on this insight, we introduce DEER, an efficient speculative decoding framework that drafts with diffusion and verifies with AR models. To enable high-quality drafting, DEER employs a two-stage training pipeline to align the dLLM-based drafters with the target AR model, and further adopts single-step decoding to generate long draft segments. Experiments show DEER reaches draft acceptance lengths of up to 32 tokens, far surpassing the 10 tokens achieved by EAGLE-3. Moreover, on HumanEval with Qwen3-30B-A3B, DEER attains a 5.54x speedup, while EAGLE-3 achieves only 2.41x. Code, model, demo, etc, will be available at https://czc726.github.io/DEER/

Group Relative Policy Optimization (GRPO) is highly effective for post-training autoregressive (AR) language models, yet its direct application to diffusion large language models (dLLMs) often triggers reward collapse. We identify two sources of incompatibility. First, GRPO relies on importance ratios defined by sequence probabilities, which are intractable in dLLMs and must be estimated (e.g., via ELBO-based or mean-field likelihood proxies), yielding inherently noisy ratios. Second, standard GRPO's formulation is not designed for estimated ratios: its conditional clipping can be anomalously bypassed by model-agnostic estimation noise, producing gradient spikes, while its fixed group-size normalization amplifies gradient-magnitude fluctuations under high-variance ratio estimates. We show these effects form a self-reinforcing instability loop that drives policy drift and further increases ratio variance. To break this loop, we propose StableDRL, a reformulation of GRPO tailored for dLLMs that uses (i) unconditional clipping to suppress outlier-induced spikes and (ii) self-normalization to constrain updates within the convex hull of per-sample gradients. We further extend StableDRL to block-wise diffusion models via a staircase attention mechanism.

In autonomous driving tasks, trajectory prediction in complex traffic environments requires adherence to real-world context conditions and behavior multimodalities. Existing methods predominantly rely on prior assumptions or generative models trained on curated data to learn road agents' stochastic behavior bounded by scene constraints. However, they often face mode averaging issues due to data imbalance and simplistic priors, and could even suffer from mode collapse due to unstable training and single ground truth supervision. These issues lead the existing methods to a loss of predictive diversity and adherence to the scene constraints. To address these challenges, we introduce a novel trajectory generator named Controllable Diffusion Trajectory (CDT), which integrates map information and social interactions into a Transformer-based conditional denoising diffusion model to guide the prediction of future trajectories. To ensure multimodality, we incorporate behavioral tokens to direct the trajectory's modes, such as going straight, turning right or left. Moreover, we incorporate the predicted endpoints as an alternative behavioral token into the CDT model to facilitate the prediction of accurate trajectories. Extensive experiments on the Argoverse 2 benchmark demonstrate that CDT excels in generating diverse and scene-compliant trajectories in complex urban settings.

Diffusion models have achieved state-of-the-art synthesis quality on both visual and audio tasks, and recent works further adapt them to textual data by diffusing on the embedding space. In this paper, we conduct systematic studies and analyze the challenges between the continuous data space and the embedding space which have not been carefully explored. Firstly, the data distribution is learnable for embeddings, which may lead to the collapse of the loss function. Secondly, as the norm of embeddings varies between popular and rare words, adding the same noise scale will lead to sub-optimal results. In addition, we find the normal level of noise causes insufficient training of the model. To address the above challenges, we propose Difformer, an embedding diffusion model based on Transformer, which consists of three essential modules including an additional anchor loss function, a layer normalization module for embeddings, and a noise factor to the Gaussian noise. Experiments on two seminal text generation tasks including machine translation and text summarization show the superiority of Difformer over compared embedding diffusion baselines.

Sampling from pretrained diffusion and flow-matching models typically requires many forward passes to generate diverse and high-fidelity images. Existing distillation methods often rely on multiple auxiliary networks, carefully designed training stages, or complex optimization pipelines. In this work, we revisit the recently proposed Drifting Model objective and show that a single drifting loss can be directly used to simplify one step distillation. A key observation is that the pretrained diffusion teacher itself already provides a strong representation space. Unlike the original Drifting Model, which relies on an additional pretrained feature extractor, we use intermediate hidden states of the pretrained teacher model as the feature representation. This removes the need for training or introducing an extra representation network while preserving a semantically meaningful feature geometry for drifting. Furthermore, we introduce a lightweight mode coverage loss to mitigate mode collapse during distillation and encourage the student generator to cover diverse teacher-supported regions. Extensive experiments on ImageNet and SDXL demonstrate that our method achieves efficient one step generation with competitive image quality and diversity, achieving FID scores of 1.58 on ImageNet-64times64 and 18.4 on SDXL, while substantially simplifying the overall distillation framework.

Most end-to-end autonomous driving methods rely on imitation learning from single expert demonstrations, often leading to conservative and homogeneous behaviors that limit generalization in complex real-world scenarios. In this work, we propose DIVER, an end-to-end driving framework that integrates reinforcement learning with diffusion-based generation to produce diverse and feasible trajectories. At the core of DIVER lies a reinforced diffusion-based generation mechanism. First, the model conditions on map elements and surrounding agents to generate multiple reference trajectories from a single ground-truth trajectory, alleviating the limitations of imitation learning that arise from relying solely on single expert demonstrations. Second, reinforcement learning is employed to guide the diffusion process, where reward-based supervision enforces safety and diversity constraints on the generated trajectories, thereby enhancing their practicality and generalization capability. Furthermore, to address the limitations of L2-based open-loop metrics in capturing trajectory diversity, we propose a novel Diversity metric to evaluate the diversity of multi-mode predictions.Extensive experiments on the closed-loop NAVSIM and Bench2Drive benchmarks, as well as the open-loop nuScenes dataset, demonstrate that DIVER significantly improves trajectory diversity, effectively addressing the mode collapse problem inherent in imitation learning.

Generative adversarial network (GAN) models can synthesize highquality audio signals while ensuring fast sample generation. However, they are difficult to train and are prone to several issues including mode collapse and divergence. In this paper, we introduce SpecDiff-GAN, a neural vocoder based on HiFi-GAN, which was initially devised for speech synthesis from mel spectrogram. In our model, the training stability is enhanced by means of a forward diffusion process which consists in injecting noise from a Gaussian distribution to both real and fake samples before inputting them to the discriminator. We further improve the model by exploiting a spectrally-shaped noise distribution with the aim to make the discriminator's task more challenging. We then show the merits of our proposed model for speech and music synthesis on several datasets. Our experiments confirm that our model compares favorably in audio quality and efficiency compared to several baselines.

Diffusion-based large language models (dLLMs) are trained flexibly to model extreme dependence in the data distribution; however, how to best utilize this information at inference time remains an open problem. In this work, we uncover an interesting property of these models: dLLMs trained on textual data implicitly learn a mixture of semi-autoregressive experts, where different generation orders reveal different specialized behaviors. We show that committing to any single, fixed inference time schedule, a common practice, collapses performance by failing to leverage this latent ensemble. To address this, we introduce HEX (Hidden semiautoregressive EXperts for test-time scaling), a training-free inference method that ensembles across heterogeneous block schedules. By doing a majority vote over diverse block-sized generation paths, HEX robustly avoids failure modes associated with any single fixed schedule. On reasoning benchmarks such as GSM8K, it boosts accuracy by up to 3.56X (from 24.72% to 88.10%), outperforming top-K margin inference and specialized fine-tuned methods like GRPO, without additional training. HEX even yields significant gains on MATH benchmark from 16.40% to 40.00%, scientific reasoning on ARC-C from 54.18% to 87.80%, and TruthfulQA from 28.36% to 57.46%. Our results establish a new paradigm for test-time scaling in diffusion-based LLMs (dLLMs), revealing that the sequence in which masking is performed plays a critical role in determining performance during inference.

Standard discrete diffusion models treat all unobserved states identically by mapping them to an absorbing [MASK] token. This creates an 'information void' where semantic information that could be inferred from unmasked tokens is lost between denoising steps. We introduce Continuously Augmented Discrete Diffusion (CADD), a framework that augments the discrete state space with a paired diffusion in a continuous latent space. This yields graded, gradually corrupted states in which masked tokens are represented by noisy yet informative latent vectors rather than collapsed 'information voids'. At each reverse step, CADD may leverage the continuous latent as a semantic hint to guide discrete denoising. The design is clean and compatible with existing discrete diffusion training. At sampling time, the strength and choice of estimator for the continuous latent vector enables a controlled trade-off between mode-coverage (generating diverse outputs) and mode-seeking (generating contextually precise outputs) behaviors. Empirically, we demonstrate CADD improves generative quality over mask-based diffusion across text generation, image synthesis, and code modeling, with consistent gains on both qualitative and quantitative metrics against strong discrete baselines.

Over the last five years, deep generative models have gradually been adopted for various tasks in biological research. Notably, image-to-image translation methods showed to be effective in revealing subtle phenotypic cell variations otherwise invisible to the human eye. Current methods to achieve this goal mainly rely on Generative Adversarial Networks (GANs). However, these models are known to suffer from some shortcomings such as training instability and mode collapse. Furthermore, the lack of robustness to invert a real image into the latent of a trained GAN prevents flexible editing of real images. In this work, we propose PhenDiff, an image-to-image translation method based on conditional diffusion models to identify subtle phenotypes in microscopy images. We evaluate this approach on biological datasets against previous work such as CycleGAN. We show that PhenDiff outperforms this baseline in terms of quality and diversity of the generated images. We then apply this method to display invisible phenotypic changes triggered by a rare neurodevelopmental disorder on microscopy images of organoids. Altogether, we demonstrate that PhenDiff is able to perform high quality biological image-to-image translation allowing to spot subtle phenotype variations on a real image.

The artificial intelligence (AI) world is running out of real data for training increasingly large generative models, resulting in accelerating pressure to train on synthetic data. Unfortunately, training new generative models with synthetic data from current or past generation models creates an autophagous (self-consuming) loop that degrades the quality and/or diversity of the synthetic data in what has been termed model autophagy disorder (MAD) and model collapse. Current thinking around model autophagy recommends that synthetic data is to be avoided for model training lest the system deteriorate into MADness. In this paper, we take a different tack that treats synthetic data differently from real data. Self-IMproving diffusion models with Synthetic data (SIMS) is a new training concept for diffusion models that uses self-synthesized data to provide negative guidance during the generation process to steer a model's generative process away from the non-ideal synthetic data manifold and towards the real data distribution. We demonstrate that SIMS is capable of self-improvement; it establishes new records based on the Fr\'echet inception distance (FID) metric for CIFAR-10 and ImageNet-64 generation and achieves competitive results on FFHQ-64 and ImageNet-512. Moreover, SIMS is, to the best of our knowledge, the first prophylactic generative AI algorithm that can be iteratively trained on self-generated synthetic data without going MAD. As a bonus, SIMS can adjust a diffusion model's synthetic data distribution to match any desired in-domain target distribution to help mitigate biases and ensure fairness.

Idempotent generative networks (IGNs) are a new line of generative models based on idempotent mapping to a target manifold. IGNs support both single-and multi-step generation, allowing for a flexible trade-off between computational cost and sample quality. But similar to Generative Adversarial Networks (GANs), conventional IGNs require adversarial training and are prone to training instabilities and mode collapse. Diffusion and score-based models are popular approaches to generative modeling that iteratively transport samples from one distribution, usually a Gaussian, to a target data distribution. These models have gained popularity due to their stable training dynamics and high-fidelity generation quality. However, this stability and quality come at the cost of high computational cost, as the data must be transported incrementally along the entire trajectory. New sampling methods, model distillation, and consistency models have been developed to reduce the sampling cost and even perform one-shot sampling from diffusion models. In this work, we unite diffusion and IGNs by distilling idempotent models from diffusion model scores, called SIGN. Our proposed method is highly stable and does not require adversarial losses. We provide a theoretical analysis of our proposed score-based training methods and empirically show that IGNs can be effectively distilled from a pre-trained diffusion model, enabling faster inference than iterative score-based models. SIGNs can perform multi-step sampling, allowing users to trade off quality for efficiency. These models operate directly on the source domain; they can project corrupted or alternate distributions back onto the target manifold, enabling zero-shot editing of inputs. We validate our models on multiple image datasets, achieving state-of-the-art results for idempotent models on the CIFAR and CelebA datasets.

This work presents self-rewarding sequential Monte Carlo (SMC), an inference-time scaling algorithm enabling effective sampling of masked diffusion language models (MDLMs). Our algorithm stems from the observation that most existing MDLMs rely on a confidence-based sampling strategy, where only tokens with the highest prediction confidence are preserved at each step. This restricts the generation to a noise-sensitive, greedy decoding paradigm, resulting in an inevitable collapse in the diversity of possible paths. We address this problem by launching multiple interacting diffusion processes in parallel, referred to as particles, for trajectory exploration. Importantly, we introduce the trajectory-level confidence as a self-rewarding signal for assigning particle importance weights. During sampling, particles are iteratively weighted and resampled to systematically steer generation towards globally confident, high-quality samples. Our self-rewarding SMC is verified on various masked diffusion language models and benchmarks, achieving significant improvement without extra training or reward guidance, while effectively converting parallel inference capacity into improved sampling quality. Our code is available at https://github.com/Algolzw/self-rewarding-smc.

Classifier-free guidance (CFG) is a fundamental tool in modern diffusion models for text-guided generation. Although effective, CFG has notable drawbacks. For instance, DDIM with CFG lacks invertibility, complicating image editing; furthermore, high guidance scales, essential for high-quality outputs, frequently result in issues like mode collapse. Contrary to the widespread belief that these are inherent limitations of diffusion models, this paper reveals that the problems actually stem from the off-manifold phenomenon associated with CFG, rather than the diffusion models themselves. More specifically, inspired by the recent advancements of diffusion model-based inverse problem solvers (DIS), we reformulate text-guidance as an inverse problem with a text-conditioned score matching loss, and develop CFG++, a novel approach that tackles the off-manifold challenges inherent in traditional CFG. CFG++ features a surprisingly simple fix to CFG, yet it offers significant improvements, including better sample quality for text-to-image generation, invertibility, smaller guidance scales, reduced mode collapse, etc. Furthermore, CFG++ enables seamless interpolation between unconditional and conditional sampling at lower guidance scales, consistently outperforming traditional CFG at all scales. Experimental results confirm that our method significantly enhances performance in text-to-image generation, DDIM inversion, editing, and solving inverse problems, suggesting a wide-ranging impact and potential applications in various fields that utilize text guidance. Project Page: https://cfgpp-diffusion.github.io/.

Diffusion models have emerged as a pivotal advancement in generative models, setting new standards to the quality of the generated instances. In the current paper we aim to underscore a discrepancy between conventional training methods and the desired conditional sampling behavior of these models. While the prevalent classifier-free guidance technique works well, it's not without flaws. At higher values for the guidance scale parameter w, we often get out of distribution samples and mode collapse, whereas at lower values for w we may not get the desired specificity. To address these challenges, we introduce an updated loss function that better aligns training objectives with sampling behaviors. Experimental validation with FID scores on CIFAR-10 elucidates our method's ability to produce higher quality samples with fewer sampling timesteps, and be more robust to the choice of guidance scale w. We also experiment with fine-tuning Stable Diffusion on the proposed loss, to provide early evidence that large diffusion models may also benefit from this refined loss function.

Autoregressive large language models achieve strong results on many benchmarks, but decoding remains fundamentally latency-limited by sequential dependence on previously generated tokens. Diffusion language models (DLMs) promise parallel generation but suffer from a fundamental static-to-dynamic misalignment: Training optimizes local transitions under fixed schedules, whereas efficient inference requires adaptive "long-jump" refinements through unseen states. Our goal is to enable highly parallel decoding for DLMs with low number of function evaluations while preserving generation quality. To achieve this, we propose CD4LM, a framework that decouples training from inference via Discrete-Space Consistency Distillation (DSCD) and Confidence-Adaptive Decoding (CAD). Unlike standard objectives, DSCD trains a student to be trajectory-invariant, mapping diverse noisy states directly to the clean distribution. This intrinsic robustness enables CAD to dynamically allocate compute resources based on token confidence, aggressively skipping steps without the quality collapse typical of heuristic acceleration. On GSM8K, CD4LM matches the LLaDA baseline with a 5.18x wall-clock speedup; across code and math benchmarks, it strictly dominates the accuracy-efficiency Pareto frontier, achieving a 3.62x mean speedup while improving average accuracy. Code is available at https://github.com/yihao-liang/CDLM

Traditionally, monocular 3D human pose estimation employs a machine learning model to predict the most likely 3D pose for a given input image. However, a single image can be highly ambiguous and induces multiple plausible solutions for the 2D-3D lifting step which results in overly confident 3D pose predictors. To this end, we propose DiffPose, a conditional diffusion model, that predicts multiple hypotheses for a given input image. In comparison to similar approaches, our diffusion model is straightforward and avoids intensive hyperparameter tuning, complex network structures, mode collapse, and unstable training. Moreover, we tackle a problem of the common two-step approach that first estimates a distribution of 2D joint locations via joint-wise heatmaps and consecutively approximates them based on first- or second-moment statistics. Since such a simplification of the heatmaps removes valid information about possibly correct, though labeled unlikely, joint locations, we propose to represent the heatmaps as a set of 2D joint candidate samples. To extract information about the original distribution from these samples we introduce our embedding transformer that conditions the diffusion model. Experimentally, we show that DiffPose slightly improves upon the state of the art for multi-hypothesis pose estimation for simple poses and outperforms it by a large margin for highly ambiguous poses.

Joint image-feature generative modeling has recently emerged as an effective strategy for improving diffusion training by coupling low-level VAE latents with high-level semantic features extracted from pre-trained visual encoders. However, existing approaches rely on a fixed representation space, constructed independently of the generative objective and kept unchanged during training. We argue that the representation space guiding diffusion should itself adapt to the generative task. To this end, we propose Coevolving Representation Diffusion (CoReDi), a framework in which the semantic representation space evolves during training by learning a lightweight linear projection jointly with the diffusion model. While naively optimizing this projection leads to degenerate solutions, we show that stable coevolution can be achieved through a combination of stop-gradient targets, normalization, and targeted regularization that prevents feature collapse. This formulation enables the semantic space to progressively specialize to the needs of image synthesis, improving its complementarity with image latents. We apply CoReDi to both VAE latent diffusion and pixel-space diffusion, demonstrating that adaptive semantic representations improve generative modeling across both settings. Experiments show that CoReDi achieves faster convergence and higher sample quality compared to joint diffusion models operating in fixed representation spaces.

Diffusion models have emerged as mainstream framework in visual generation. Building upon this success, the integration of Mixture of Experts (MoE) methods has shown promise in enhancing model scalability and performance. In this paper, we introduce Race-DiT, a novel MoE model for diffusion transformers with a flexible routing strategy, Expert Race. By allowing tokens and experts to compete together and select the top candidates, the model learns to dynamically assign experts to critical tokens. Additionally, we propose per-layer regularization to address challenges in shallow layer learning, and router similarity loss to prevent mode collapse, ensuring better expert utilization. Extensive experiments on ImageNet validate the effectiveness of our approach, showcasing significant performance gains while promising scaling properties.

Reinforcement learning (RL) has shown extraordinary potential in aligning diffusion models to downstream tasks, yet most of them still suffer from significant reward hacking, which degrades generative diversity and quality by inducing visual mode collapse and amplifying unreliable rewards. We identify the root cause as the mode-seeking nature of these methods, which maximize expected reward without effectively constraining probability distribution over acceptable trajectories, causing concentration on a few high-reward paths. In contrast, we propose Trajectory Matching Policy Optimization (TMPO), which replaces scalar reward maximization with trajectory-level reward distribution matching. Specifically, TMPO introduces a Softmax Trajectory Balance (Softmax-TB) objective to match the policy probabilities of K trajectories to a reward-induced Boltzmann distribution. We prove that this objective inherits the mode-covering property of forward KL divergence, preserving coverage over all acceptable trajectories while optimizing reward. To further reduce multi-trajectory training time on large-scale flow-matching models, TMPO incorporates Dynamic Stochastic Tree Sampling, where trajectories share denoising prefixes and branch at dynamically scheduled steps, reducing redundant computation while improving training effectiveness. Extensive results across diverse alignment tasks such as human preference, compositional generation and text rendering show that TMPO improves generative diversity over state-of-the-art methods by 9.1%, and achieves competitive performance in all downstream and efficiency metrics, attaining the optimal trade-off between reward and diversity.

Recent reinforcement learning (RL) methods improve LLM reasoning by optimizing discrete Chain-of-Thought (CoT) generation; however, exploration in token space often suffers from diversity collapse as policy entropy decreases due to mode elicitation behavior in discrete RL. To mitigate this issue, we propose Latent Diffusion Reasoning with Reinforcement Learning (LaDi-RL), a framework that conducts exploration directly in a continuous latent space, where latent variables encode semantic-level reasoning trajectories. By modeling exploration via guided diffusion, multi-step denoising distributes stochasticity and preserves multiple coexisting solution modes without mutual suppression. Furthermore, by decoupling latent-space exploration from text-space generation, we show that latent diffusion-based optimization is more effective than text-space policy optimization alone, while a complementary text policy provides additional gains when combined with latent exploration. Experiments on code generation and mathematical reasoning benchmarks demonstrate consistent improvements in both pass@1 and pass@k over discrete RL baselines, with absolute pass@1 gains of +9.4% on code generation and +5.7% on mathematical reasoning, highlighting diffusion-based latent RL as a principled alternative to discrete token-level RL for reasoning.

Diffusion language models (DLMs) are emerging as a powerful and promising alternative to the dominant autoregressive paradigm, offering inherent advantages in parallel generation and bidirectional context modeling. However, the performance of DLMs on code generation tasks, which have stronger structural constraints, is significantly hampered by the critical trade-off between inference speed and output quality. We observed that accelerating the code generation process by reducing the number of sampling steps usually leads to a catastrophic collapse in performance. In this paper, we introduce efficient Sampling with Adaptive acceleration and Backtracking Enhanced Remasking (i.e., Saber), a novel training-free sampling algorithm for DLMs to achieve better inference speed and output quality in code generation. Specifically, Saber is motivated by two key insights in the DLM generation process: 1) it can be adaptively accelerated as more of the code context is established; 2) it requires a backtracking mechanism to reverse the generated tokens. Extensive experiments on multiple mainstream code generation benchmarks show that Saber boosts Pass@1 accuracy by an average improvement of 1.9% over mainstream DLM sampling methods, meanwhile achieving an average 251.4% inference speedup. By leveraging the inherent advantages of DLMs, our work significantly narrows the performance gap with autoregressive models in code generation.

The generation of high-quality, long-sequenced time-series data is essential due to its wide range of applications. In the past, standalone Recurrent and Convolutional Neural Network-based Generative Adversarial Networks (GAN) were used to synthesize time-series data. However, they are inadequate for generating long sequences of time-series data due to limitations in the architecture. Furthermore, GANs are well known for their training instability and mode collapse problem. To address this, we propose TransFusion, a diffusion, and transformers-based generative model to generate high-quality long-sequence time-series data. We have stretched the sequence length to 384, and generated high-quality synthetic data. Also, we introduce two evaluation metrics to evaluate the quality of the synthetic data as well as its predictive characteristics. We evaluate TransFusion with a wide variety of visual and empirical metrics, and TransFusion outperforms the previous state-of-the-art by a significant margin.

We introduce Multi-view Ancestral Sampling (MAS), a method for generating consistent multi-view 2D samples of a motion sequence, enabling the creation of its 3D counterpart. MAS leverages a diffusion model trained solely on 2D data, opening opportunities to exciting and diverse fields of motion previously under-explored as 3D data is scarce and hard to collect. MAS works by simultaneously denoising multiple 2D motion sequences representing the same motion from different angles. Our consistency block ensures consistency across all views at each diffusion step by combining the individual generations into a unified 3D sequence, and projecting it back to the original views for the next iteration. We demonstrate MAS on 2D pose data acquired from videos depicting professional basketball maneuvers, rhythmic gymnastic performances featuring a ball apparatus, and horse obstacle course races. In each of these domains, 3D motion capture is arduous, and yet, MAS generates diverse and realistic 3D sequences without textual conditioning. As we demonstrate, our ancestral sampling-based approach offers a more natural integration with the diffusion framework compared to popular denoising optimization-based approaches, and avoids common issues such as out-of-domain sampling, lack of details and mode-collapse. https://guytevet.github.io/mas-page/

Diffusion models produce impressive results in modalities ranging from images and video to protein design and text. However, generating samples with user-specified properties remains a challenge. Recent research proposes fine-tuning models to maximize rewards that capture desired properties, but these methods require expensive training and are prone to mode collapse. In this work, we propose Feynman Kac (FK) steering, an inference-time framework for steering diffusion models with reward functions. FK steering works by sampling a system of multiple interacting diffusion processes, called particles, and resampling particles at intermediate steps based on scores computed using functions called potentials. Potentials are defined using rewards for intermediate states and are selected such that a high value indicates that the particle will yield a high-reward sample. We explore various choices of potentials, intermediate rewards, and samplers. We evaluate FK steering on text-to-image and text diffusion models. For steering text-to-image models with a human preference reward, we find that FK steering a 0.8B parameter model outperforms a 2.6B parameter fine-tuned model on prompt fidelity, with faster sampling and no training. For steering text diffusion models with rewards for text quality and specific text attributes, we find that FK steering generates lower perplexity, more linguistically acceptable outputs and enables gradient-free control of attributes like toxicity. Our results demonstrate that inference-time scaling and steering of diffusion models, even with off-the-shelf rewards, can provide significant sample quality gains and controllability benefits. Code is available at https://github.com/zacharyhorvitz/Fk-Diffusion-Steering .

Pixel-space diffusion models are trained on full-bandwidth noisy images, yet the useful signal available to the denoiser is strongly frequency dependent. Under rectified-flow diffusion and natural-image power-law spectra, the per-band data-to-noise contour k^{*}(t) = (1-t)^{-2/α} separates a signal-bearing low-frequency region from a noise-dominated high-frequency region at each time t. We show that this implicit coarse-to-fine structure is not merely descriptive: it induces a capacity-allocation problem. A standard pixel-space denoiser must discover the moving bandwidth boundary internally and can spend computation on frequency-time regions where the optimal prediction collapses to deterministic baselines rather than data-distribution modeling. To make this boundary explicit, we introduce Spectral Forcing, a parameter-free, time-conditional 2D-DCT low-pass operator applied to the noisy input before the patch embedder. Its cutoff expands monotonically with the diffusion time and becomes the identity at the data endpoint. Through controlled synthetic experiments, we identify the regime in which the operator is beneficial: coarse patch tokenization and data whose high-frequency content is predominantly noise rather than essential signal. On ImageNet-256 with JiT-700M/32, Spectral Forcing consistently improves both FID and Inception Score across different training epochs, demonstrating robust gains throughout training; at finer tokenization, the spectral forcing is still competitive. We further insert the unchanged operator into SenseNova-U1, a unified text-to-image model, where it improves DPG-Bench and GenEval, showing that the input-side spectral prior transfers beyond class-conditional generation. These results suggest a route to capacity-efficient pixel-space diffusion by showing the signal and hiding the noise.

Diffusion models produce high-quality text-to-image results, but their iterative denoising is computationally expensive.Distribution Matching Distillation (DMD) emerges as a promising path to few-step distillation, but suffers from diversity collapse and fidelity degradation when reduced to two steps or fewer. We present 1.x-Distill, the first fractional-step distillation framework that breaks the integer-step constraint of prior few-step methods and establishes 1.x-step generation as a practical regime for distilled diffusion models.Specifically, we first analyze the overlooked role of teacher CFG in DMD and introduce a simple yet effective modification to suppress mode collapse. Then, to improve performance under extreme steps, we introduce Stagewise Focused Distillation, a two-stage strategy that learns coarse structure through diversity-preserving distribution matching and refines details with inference-consistent adversarial distillation. Furthermore, we design a lightweight compensation module for Distill--Cache co-Training, which naturally incorporates block-level caching into our distillation pipeline.Experiments on SD3-Medium and SD3.5-Large show that 1.x-Distill surpasses prior few-step methods, achieving better quality and diversity at 1.67 and 1.74 effective NFEs, respectively, with up to 33x speedup over original 28x2 NFE sampling.

Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, f:XtoY. Is it possible to identify a pair of non-standard vector spaces for which a conventionally nonlinear function is, in fact, linear? This paper introduces a method that makes such vector spaces explicit by construction. We find that if we sandwich a linear operator A between two invertible neural networks, f(x)=g_y^{-1}(A g_x(x)), then the corresponding vector spaces X and Y are induced by newly defined addition and scaling actions derived from g_x and g_y. We term this kind of architecture a Linearizer. This framework makes the entire arsenal of linear algebra, including SVD, pseudo-inverse, orthogonal projection and more, applicable to nonlinear mappings. Furthermore, we show that the composition of two Linearizers that share a neural network is also a Linearizer. We leverage this property and demonstrate that training diffusion models using our architecture makes the hundreds of sampling steps collapse into a single step. We further utilize our framework to enforce idempotency (i.e. f(f(x))=f(x)) on networks leading to a globally projective generative model and to demonstrate modular style transfer.

One-hot vectors, a common method for representing discrete/categorical data, in machine learning are widely used because of their simplicity and intuitiveness. However, one-hot vectors suffer from a linear increase in dimensionality, posing computational and memory challenges, especially when dealing with datasets containing numerous categories. In this paper, we focus on tabular data generation, and reveal the multinomial diffusion faces the mode collapse phenomenon when the cardinality is high. Moreover, due to the limitations of one-hot vectors, the training phase takes time longer in such a situation. To address these issues, we propose Residual Bit Vectors (ResBit), a technique for densely representing categorical data. ResBit is an extension of analog bits and overcomes limitations of analog bits when applied to tabular data generation. Our experiments demonstrate that ResBit not only accelerates training but also maintains performance when compared with the situations before applying ResBit. Furthermore, our results indicate that many existing methods struggle with high-cardinality data, underscoring the need for lower-dimensional representations, such as ResBit and latent vectors.

We formalize action emergence as a target capability for end-to-end autonomous driving: the ability to generate physically feasible, semantically appropriate, and safety-compliant actions in arbitrary, long-tail traffic scenes through scene-conditioned reasoning rather than retrieval or interpolation of learned scene-action mappings. We show that previous paradigms cannot deliver action emergence: autoregressive trajectory decoders collapse the inherently multimodal future into a single averaged output, while diffusion and flow-matching generators express multimodality but are not steerable by reasoned intent. We propose Streaming Intent as a concrete way to approach action emergence: a mechanism that makes driving intent (i) semantically streamed through a continuous chain-of-thought that causally derives the intent from scene understanding, and (ii) temporally streamed across clips so that intent commitments remain coherent along the driving horizon. We realize Streaming Intent in a VLA model we call SI (Streaming Intent). SI autoregressively decodes a four-step chain-of-thought and emits an intent token; the decoded intent then drives classifier-free guidance (CFG) on a flow-matching action head, requiring only two denoising steps to generate the final trajectory. On the Waymo End-to-End benchmark, SI achieves competitive aggregate performance, with an RFS score of 7.96 on the validation set and 7.74 on the test set. Beyond aggregate metrics, the model demonstrates -- to our knowledge for the first time in a fully end-to-end VLA -- intent-faithful controllability: for a fixed scene, varying the intent class at inference yields qualitatively distinct yet consistently high-quality plans, arising purely from data-driven learning without any pre-built trajectory bank or hand-coded post-hoc selector.

Generative models for structure-based drug design (SBDD) have shown promising results in recent years. Existing works mainly focus on how to generate molecules with higher binding affinity, ignoring the feasibility prerequisites for generated 3D poses and resulting in false positives. We conduct thorough studies on key factors of ill-conformational problems when applying autoregressive methods and diffusion to SBDD, including mode collapse and hybrid continuous-discrete space. In this paper, we introduce MolCRAFT, the first SBDD model that operates in the continuous parameter space, together with a novel noise reduced sampling strategy. Empirical results show that our model consistently achieves superior performance in binding affinity with more stable 3D structure, demonstrating our ability to accurately model interatomic interactions. To our best knowledge, MolCRAFT is the first to achieve reference-level Vina Scores (-6.59 kcal/mol) with comparable molecular size, outperforming other strong baselines by a wide margin (-0.84 kcal/mol). Code is available at https://github.com/AlgoMole/MolCRAFT.

Visual Autoregressive (VAR) models have recently garnered significant attention for their innovative next-scale prediction paradigm, offering notable advantages in both inference efficiency and image quality compared to traditional multi-step autoregressive (AR) and diffusion models. However, despite their efficiency, VAR models often suffer from the diversity collapse i.e., a reduction in output variability, analogous to that observed in few-step distilled diffusion models. In this paper, we introduce DiverseVAR, a simple yet effective approach that restores the generative diversity of VAR models without requiring any additional training. Our analysis reveals the pivotal component of the feature map as a key factor governing diversity formation at early scales. By suppressing the pivotal component in the model input and amplifying it in the model output, DiverseVAR effectively unlocks the inherent generative potential of VAR models while preserving high-fidelity synthesis. Empirical results demonstrate that our approach substantially enhances generative diversity with only neglectable performance influences. Our code will be publicly released at https://github.com/wangtong627/DiverseVAR.

Text-to-Motion (T2M) generation aims to synthesize realistic and semantically aligned human motion sequences from natural language descriptions. However, current approaches face dual challenges: Generative models (e.g., diffusion models) suffer from limited diversity, error accumulation, and physical implausibility, while Retrieval-Augmented Generation (RAG) methods exhibit diffusion inertia, partial-mode collapse, and asynchronous artifacts. To address these limitations, we propose ReMoMask, a unified framework integrating three key innovations: 1) A Bidirectional Momentum Text-Motion Model decouples negative sample scale from batch size via momentum queues, substantially improving cross-modal retrieval precision; 2) A Semantic Spatio-temporal Attention mechanism enforces biomechanical constraints during part-level fusion to eliminate asynchronous artifacts; 3) RAG-Classier-Free Guidance incorporates minor unconditional generation to enhance generalization. Built upon MoMask's RVQ-VAE, ReMoMask efficiently generates temporally coherent motions in minimal steps. Extensive experiments on standard benchmarks demonstrate the state-of-the-art performance of ReMoMask, achieving a 3.88% and 10.97% improvement in FID scores on HumanML3D and KIT-ML, respectively, compared to the previous SOTA method RAG-T2M. Code: https://github.com/AIGeeksGroup/ReMoMask. Website: https://aigeeksgroup.github.io/ReMoMask.

This paper introduces ViscoNet, a novel method that enhances text-to-image human generation models with visual prompting. Unlike existing methods that rely on lengthy text descriptions to control the image structure, ViscoNet allows users to specify the visual appearance of the target object with a reference image. ViscoNet disentangles the object's appearance from the image background and injects it into a pre-trained latent diffusion model (LDM) model via a ControlNet branch. This way, ViscoNet mitigates the style mode collapse problem and enables precise and flexible visual control. We demonstrate the effectiveness of ViscoNet on human image generation, where it can manipulate visual attributes and artistic styles with text and image prompts. We also show that ViscoNet can learn visual conditioning from small and specific object domains while preserving the generative power of the LDM backbone.

Text-to-motion generation is a formidable task, aiming to produce human motions that align with the input text while also adhering to human capabilities and physical laws. While there have been advancements in diffusion models, their application in discrete spaces remains underexplored. Current methods often overlook the varying significance of different motions, treating them uniformly. It is essential to recognize that not all motions hold the same relevance to a particular textual description. Some motions, being more salient and informative, should be given precedence during generation. In response, we introduce a Priority-Centric Motion Discrete Diffusion Model (M2DM), which utilizes a Transformer-based VQ-VAE to derive a concise, discrete motion representation, incorporating a global self-attention mechanism and a regularization term to counteract code collapse. We also present a motion discrete diffusion model that employs an innovative noise schedule, determined by the significance of each motion token within the entire motion sequence. This approach retains the most salient motions during the reverse diffusion process, leading to more semantically rich and varied motions. Additionally, we formulate two strategies to gauge the importance of motion tokens, drawing from both textual and visual indicators. Comprehensive experiments on the HumanML3D and KIT-ML datasets confirm that our model surpasses existing techniques in fidelity and diversity, particularly for intricate textual descriptions.

Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism of particle's motion in expanding medium has only been investigated in the framework of continuous-time random walk. To focus on more diffusion processes and physical observables, we build the Langevin picture of anomalous diffusion in expanding medium, and conduct detailed analyses in the framework of Langevin equation. With the help of a subordinator, both subdiffusion process and superdiffusion process in expanding medium are discussed. We find that the expanding medium with different changing rate (exponential form and power-law form) leads to quite different diffusion phenomena. The particle's intrinsic diffusion behavior also plays an important role. Our detailed theoretical analyses and simulations present a panoramic view of investigating anomalous diffusion in expanding medium under the framework of Langevin equation.

Diffusion models, which learn to reverse a signal destruction process to generate new data, typically require the signal at each step to have the same dimension. We argue that, considering the spatial redundancy in image signals, there is no need to maintain a high dimensionality in the evolution process, especially in the early generation phase. To this end, we make a theoretical generalization of the forward diffusion process via signal decomposition. Concretely, we manage to decompose an image into multiple orthogonal components and control the attenuation of each component when perturbing the image. That way, along with the noise strength increasing, we are able to diminish those inconsequential components and thus use a lower-dimensional signal to represent the source, barely losing information. Such a reformulation allows to vary dimensions in both training and inference of diffusion models. Extensive experiments on a range of datasets suggest that our approach substantially reduces the computational cost and achieves on-par or even better synthesis performance compared to baseline methods. We also show that our strategy facilitates high-resolution image synthesis and improves FID of diffusion model trained on FFHQ at 1024times1024 resolution from 52.40 to 10.46. Code and models will be made publicly available.

This monograph presents the core principles that have guided the development of diffusion models, tracing their origins and showing how diverse formulations arise from shared mathematical ideas. Diffusion modeling starts by defining a forward process that gradually corrupts data into noise, linking the data distribution to a simple prior through a continuum of intermediate distributions. The goal is to learn a reverse process that transforms noise back into data while recovering the same intermediates. We describe three complementary views. The variational view, inspired by variational autoencoders, sees diffusion as learning to remove noise step by step. The score-based view, rooted in energy-based modeling, learns the gradient of the evolving data distribution, indicating how to nudge samples toward more likely regions. The flow-based view, related to normalizing flows, treats generation as following a smooth path that moves samples from noise to data under a learned velocity field. These perspectives share a common backbone: a time-dependent velocity field whose flow transports a simple prior to the data. Sampling then amounts to solving a differential equation that evolves noise into data along a continuous trajectory. On this foundation, the monograph discusses guidance for controllable generation, efficient numerical solvers, and diffusion-motivated flow-map models that learn direct mappings between arbitrary times. It provides a conceptual and mathematically grounded understanding of diffusion models for readers with basic deep-learning knowledge.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

Modern deep neural networks have achieved impressive performance on tasks from image classification to natural language processing. Surprisingly, these complex systems with massive amounts of parameters exhibit the same structural properties in their last-layer features and classifiers across canonical datasets when training until convergence. In particular, it has been observed that the last-layer features collapse to their class-means, and those class-means are the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is known as Neural Collapse (NC). Recent papers have theoretically shown that NC emerges in the global minimizers of training problems with the simplified "unconstrained feature model". In this context, we take a step further and prove the NC occurrences in deep linear networks for the popular mean squared error (MSE) and cross entropy (CE) losses, showing that global solutions exhibit NC properties across the linear layers. Furthermore, we extend our study to imbalanced data for MSE loss and present the first geometric analysis of NC under bias-free setting. Our results demonstrate the convergence of the last-layer features and classifiers to a geometry consisting of orthogonal vectors, whose lengths depend on the amount of data in their corresponding classes. Finally, we empirically validate our theoretical analyses on synthetic and practical network architectures with both balanced and imbalanced scenarios.

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Diffusion models have been central to the development of recent image, video, and even text generation systems. They posses striking geometric properties that can be faithfully portrayed in low-dimensional settings. However, existing resources for explaining diffusion either require an advanced theoretical foundation or focus on their neural network architectures rather than their rich geometric properties. We introduce Diffusion Explorer, an interactive tool to explain the geometric properties of diffusion models. Users can train 2D diffusion models in the browser and observe the temporal dynamics of their sampling process. Diffusion Explorer leverages interactive animation, which has been shown to be a powerful tool for making engaging visualizations of dynamic systems, making it well suited to explaining diffusion models which represent stochastic processes that evolve over time. Diffusion Explorer is open source and a live demo is available at alechelbling.com/Diffusion-Explorer.

In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion models inherently perform evolutionary algorithms, naturally encompassing selection, mutation, and reproductive isolation. Building on this equivalence, we propose the Diffusion Evolution method: an evolutionary algorithm utilizing iterative denoising -- as originally introduced in the context of diffusion models -- to heuristically refine solutions in parameter spaces. Unlike traditional approaches, Diffusion Evolution efficiently identifies multiple optimal solutions and outperforms prominent mainstream evolutionary algorithms. Furthermore, leveraging advanced concepts from diffusion models, namely latent space diffusion and accelerated sampling, we introduce Latent Space Diffusion Evolution, which finds solutions for evolutionary tasks in high-dimensional complex parameter space while significantly reducing computational steps. This parallel between diffusion and evolution not only bridges two different fields but also opens new avenues for mutual enhancement, raising questions about open-ended evolution and potentially utilizing non-Gaussian or discrete diffusion models in the context of Diffusion Evolution.

Diffusion models have recently been increasingly applied to temporal data such as video, fluid mechanics simulations, or climate data. These methods generally treat subsequent frames equally regarding the amount of noise in the diffusion process. This paper explores Rolling Diffusion: a new approach that uses a sliding window denoising process. It ensures that the diffusion process progressively corrupts through time by assigning more noise to frames that appear later in a sequence, reflecting greater uncertainty about the future as the generation process unfolds. Empirically, we show that when the temporal dynamics are complex, Rolling Diffusion is superior to standard diffusion. In particular, this result is demonstrated in a video prediction task using the Kinetics-600 video dataset and in a chaotic fluid dynamics forecasting experiment.

Diffusion models are a family of generative models that yield record-breaking performance in tasks such as image synthesis, video generation, and molecule design. Despite their capabilities, their efficiency, especially in the reverse denoising process, remains a challenge due to slow convergence rates and high computational costs. In this work, we introduce an approach that leverages continuous dynamical systems to design a novel denoising network for diffusion models that is more parameter-efficient, exhibits faster convergence, and demonstrates increased noise robustness. Experimenting with denoising probabilistic diffusion models, our framework operates with approximately a quarter of the parameters and 30% of the Floating Point Operations (FLOPs) compared to standard U-Nets in Denoising Diffusion Probabilistic Models (DDPMs). Furthermore, our model is up to 70% faster in inference than the baseline models when measured in equal conditions while converging to better quality solutions.

Diffusion models degrade images through noise, and reversing this process reveals an information hierarchy across timesteps. Scale-space theory exhibits a similar hierarchy via low-pass filtering. We formalize this connection and show that highly noisy diffusion states contain no more information than small, downsampled images - raising the question of why they must be processed at full resolution. To address this, we fuse scale spaces into the diffusion process by formulating a family of diffusion models with generalized linear degradations and practical implementations. Using downsampling as the degradation yields our proposed Scale Space Diffusion. To support Scale Space Diffusion, we introduce Flexi-UNet, a UNet variant that performs resolution-preserving and resolution-increasing denoising using only the necessary parts of the network. We evaluate our framework on CelebA and ImageNet and analyze its scaling behavior across resolutions and network depths. Our project website ( https://prateksha.github.io/projects/scale-space-diffusion/ ) is available publicly.

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce ``Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

Diffusion models, which employ stochastic differential equations to sample images through integrals, have emerged as a dominant class of generative models. However, the rationality of the diffusion process itself receives limited attention, leaving the question of whether the problem is well-posed and well-conditioned. In this paper, we uncover a vexing propensity of diffusion models: they frequently exhibit the infinite Lipschitz near the zero point of timesteps. This poses a threat to the stability and accuracy of the diffusion process, which relies on integral operations. We provide a comprehensive evaluation of the issue from both theoretical and empirical perspectives. To address this challenge, we propose a novel approach, dubbed E-TSDM, which eliminates the Lipschitz singularity of the diffusion model near zero. Remarkably, our technique yields a substantial improvement in performance, e.g., on the high-resolution FFHQ dataset (256times256). Moreover, as a byproduct of our method, we manage to achieve a dramatic reduction in the Frechet Inception Distance of other acceleration methods relying on network Lipschitz, including DDIM and DPM-Solver, by over 33%. We conduct extensive experiments on diverse datasets to validate our theory and method. Our work not only advances the understanding of the general diffusion process, but also provides insights for the design of diffusion models.

We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept.

Every Cartesian three-dimensional PDE solver hides a structural secret that production CFD codes have used for half a century and that graduate-level textbooks rarely state plainly. The derivative matrices, the compact Padé line solves, the Galerkin mass inversions, the alternating-direction-implicit substeps, and even the fast Poisson and Helmholtz diagonalization transforms all factor along the coordinate axes and collapse into repeated one-dimensional banded kernels executed along the grid lines. The three-dimensional operator exists only on paper; it is never assembled, factored, or stored. This paper is the manual for that collapse. We derive the Kronecker-product algebra that makes it exact, carry it cleanly through central differences, compact schemes, tensor-product Galerkin, B-spline and isogeometric methods, collocation, ADI time stepping, and direct Poisson and Helmholtz solves, and bring into the open the three production tricks that turn the reduction into hardware-conscious floating-point throughput on real machines: the multi-right-hand-side reshape that exposes a sweep as one batched line kernel (a dense BLAS-3 GEMM when the line factor is dense or element-local, a banded or stencil kernel when it is not), the sum factorization that rescues high-order Galerkin from the O(p^{2d}) quadrature trap, and the pencil decomposition that keeps every direction contiguous across an MPI cluster. For fixed stencil width or fixed polynomial degree, the compute cost stays O(N) in the total number of unknowns N = N_x N_y N_z; the operator storage drops to O(N_x + N_y + N_z) up to bandwidth constants; direct separable Poisson and Helmholtz solvers add the expected transform cost; the line kernels are embarrassingly parallel. These facts are familiar to practitioners but rarely assembled in one place; this paper collects them and shows how to use them.

The study conducted by Shumailov et al. (2024) demonstrates that repeatedly training a generative model on synthetic data leads to model collapse. This finding has generated considerable interest and debate, particularly given that current models have nearly exhausted the available data. In this work, we investigate the effects of fitting a distribution (through Kernel Density Estimation, or KDE) or a model to the data, followed by repeated sampling from it. Our objective is to develop a theoretical understanding of the phenomenon observed by Shumailov et al. (2024). Our results indicate that the outcomes reported are a statistical phenomenon and may be unavoidable.

In the era of proliferation of large language and image generation models, the phenomenon of "model collapse" refers to the situation whereby as a model is trained recursively on data generated from previous generations of itself over time, its performance degrades until the model eventually becomes completely useless, i.e the model collapses. In this work, we study this phenomenon in the setting of high-dimensional regression and obtain analytic formulae which quantitatively outline this phenomenon in a broad range of regimes. In the special case of polynomial decaying spectral and source conditions, we obtain modified scaling laws which exhibit new crossover phenomena from fast to slow rates. We also propose a simple strategy based on adaptive regularization to mitigate model collapse. Our theoretical results are validated with experiments.

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical understanding of their observed properties is still lacking, in particular, their weak sensitivity to the choice of noise family and the role of adequate scheduling of noise levels for good synthesis. By identifying a correspondence between diffusion models and a well-known paradigm in cognitive science known as serial reproduction, whereby human agents iteratively observe and reproduce stimuli from memory, we show how the aforementioned properties of diffusion models can be explained as a natural consequence of this correspondence. We then complement our theoretical analysis with simulations that exhibit these key features. Our work highlights how classic paradigms in cognitive science can shed light on state-of-the-art machine learning problems.

How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that underlies image generation has the following properties: (i) individual trajectories tend to be low-dimensional and resemble 2D `rotations'; (ii) high-variance scene features like layout tend to emerge earlier, while low-variance details tend to emerge later; and (iii) early perturbations tend to have a greater impact on image content than later perturbations. To understand these phenomena, we derive and study a closed-form solution to the probability flow ODE for a Gaussian distribution, which shows that the reverse diffusion state rotates towards a gradually-specified target on the image manifold. It also shows that generation involves first committing to an outline, and then to finer and finer details. We find that this solution accurately describes the initial phase of image generation for pretrained models, and can in principle be used to make image generation more efficient by skipping reverse diffusion steps. Finally, we use our solution to characterize the image manifold in Stable Diffusion. Our viewpoint reveals an unexpected similarity between generation by GANs and diffusion and provides a conceptual link between diffusion and image retrieval.

Latent Diffusion Models (LDMs) achieve high-fidelity synthesis but suffer from latent space brittleness, causing discontinuous semantic jumps during editing. We introduce a Riemannian framework to diagnose this instability by analyzing the generative Jacobian, decomposing geometry into Local Scaling (capacity) and Local Complexity (curvature). Our study uncovers a ``Geometric Decoupling": while curvature in normal generation functionally encodes image detail, OOD generation exhibits a functional decoupling where extreme curvature is wasted on unstable semantic boundaries rather than perceptible details. This geometric misallocation identifies ``Geometric Hotspots" as the structural root of instability, providing a robust intrinsic metric for diagnosing generative reliability.

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much more amenable to computation. By leveraging and combining various ans\"{a}tze, we can quickly compute relevant quantities to high precision. On low dimensional datasets, our correction produces a noticeable improvement, allowing diffusion to compete with other methods. Additionally, we show that our method enables us to scale to high dimensional tasks on nontrivial manifolds. In particular, we model QCD densities on SU(n) lattices and contrastively learned embeddings on high dimensional hyperspheres.

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic optimization perspective for both faster training and sampling. We first find that the diffusion process of DMs accords with the stochastic optimization process of stochastic gradient descent (SGD) on a stochastic time-variant problem. Then, inspired by momentum SGD that uses both gradient and an extra momentum to achieve faster and more stable convergence than SGD, we integrate momentum into the diffusion process of DMs. This comes with a unique challenge of deriving the noise perturbation kernel from the momentum-based diffusion process. To this end, we frame the process as a Damped Oscillation system whose critically damped state -- the kernel solution -- avoids oscillation and yields a faster convergence speed of the diffusion process. Empirical results show that our FDM can be applied to several popular DM frameworks, e.g., VP, VE, and EDM, and reduces their training cost by about 50% with comparable image synthesis performance on CIFAR-10, FFHQ, and AFHQv2 datasets. Moreover, FDM decreases their sampling steps by about 3x to achieve similar performance under the same samplers. The code is available at https://github.com/sail-sg/FDM.

Diffusion models achieved great success in image synthesis, but still face challenges in high-resolution generation. Through the lens of discrete cosine transformation, we find the main reason is that the same noise level on a higher resolution results in a higher Signal-to-Noise Ratio in the frequency domain. In this work, we present Relay Diffusion Model (RDM), which transfers a low-resolution image or noise into an equivalent high-resolution one for diffusion model via blurring diffusion and block noise. Therefore, the diffusion process can continue seamlessly in any new resolution or model without restarting from pure noise or low-resolution conditioning. RDM achieves state-of-the-art FID on CelebA-HQ and sFID on ImageNet 256times256, surpassing previous works such as ADM, LDM and DiT by a large margin. All the codes and checkpoints are open-sourced at https://github.com/THUDM/RelayDiffusion.

Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

In recent years, denoising diffusion models have become a crucial area of research due to their abundance in the rapidly expanding field of generative AI. While recent statistical advances have delivered explanations for the generation ability of idealised denoising diffusion models for high-dimensional target data, implementations introduce thresholding procedures for the generating process to overcome issues arising from the unbounded state space of such models. This mismatch between theoretical design and implementation of diffusion models has been addressed empirically by using a reflected diffusion process as the driver of noise instead. In this paper, we study statistical guarantees of these denoising reflected diffusion models. In particular, we establish minimax optimal rates of convergence in total variation, up to a polylogarithmic factor, under Sobolev smoothness assumptions. Our main contributions include the statistical analysis of this novel class of denoising reflected diffusion models and a refined score approximation method in both time and space, leveraging spectral decomposition and rigorous neural network analysis.

The Cambrian explosion of easily accessible pre-trained diffusion models suggests a demand for methods that combine multiple different pre-trained diffusion models without incurring the significant computational burden of re-training a larger combined model. In this paper, we cast the problem of combining multiple pre-trained diffusion models at the generation stage under a novel proposed framework termed superposition. Theoretically, we derive superposition from rigorous first principles stemming from the celebrated continuity equation and design two novel algorithms tailor-made for combining diffusion models in SuperDiff. SuperDiff leverages a new scalable It\^o density estimator for the log likelihood of the diffusion SDE which incurs no additional overhead compared to the well-known Hutchinson's estimator needed for divergence calculations. We demonstrate that SuperDiff is scalable to large pre-trained diffusion models as superposition is performed solely through composition during inference, and also enjoys painless implementation as it combines different pre-trained vector fields through an automated re-weighting scheme. Notably, we show that SuperDiff is efficient during inference time, and mimics traditional composition operators such as the logical OR and the logical AND. We empirically demonstrate the utility of using SuperDiff for generating more diverse images on CIFAR-10, more faithful prompt conditioned image editing using Stable Diffusion, and improved unconditional de novo structure design of proteins. https://github.com/necludov/super-diffusion

Observing certain patches in an image reduces the uncertainty of others. Their realization lowers the distribution entropy of each remaining patch feature, analogous to collapsing a particle's wave function in quantum mechanics. This phenomenon can intuitively be called patch collapse. To identify which patches are most relied on during a target region's collapse, we learn an autoencoder that softly selects a subset of patches to reconstruct each target patch. Graphing these learned dependencies for each patch's PageRank score reveals the optimal patch order to realize an image. We show that respecting this order benefits various masked image modeling methods. First, autoregressive image generation can be boosted by retraining the state-of-the-art model MAR. Next, we introduce a new setup for image classification by exposing Vision Transformers only to high-rank patches in the collapse order. Seeing 22\% of such patches is sufficient to achieve high accuracy. With these experiments, we propose patch collapse as a novel image modeling perspective that promotes vision efficiency. Our project is available at https://github.com/wguo-ai/CoP .

A diffusion probabilistic model (DPM), which constructs a forward diffusion process by gradually adding noise to data points and learns the reverse denoising process to generate new samples, has been shown to handle complex data distribution. Despite its recent success in image synthesis, applying DPMs to video generation is still challenging due to high-dimensional data spaces. Previous methods usually adopt a standard diffusion process, where frames in the same video clip are destroyed with independent noises, ignoring the content redundancy and temporal correlation. This work presents a decomposed diffusion process via resolving the per-frame noise into a base noise that is shared among all frames and a residual noise that varies along the time axis. The denoising pipeline employs two jointly-learned networks to match the noise decomposition accordingly. Experiments on various datasets confirm that our approach, termed as VideoFusion, surpasses both GAN-based and diffusion-based alternatives in high-quality video generation. We further show that our decomposed formulation can benefit from pre-trained image diffusion models and well-support text-conditioned video creation.

We discover that common diffusion noise schedules do not enforce the last timestep to have zero signal-to-noise ratio (SNR), and some implementations of diffusion samplers do not start from the last timestep. Such designs are flawed and do not reflect the fact that the model is given pure Gaussian noise at inference, creating a discrepancy between training and inference. We show that the flawed design causes real problems in existing implementations. In Stable Diffusion, it severely limits the model to only generate images with medium brightness and prevents it from generating very bright and dark samples. We propose a few simple fixes: (1) rescale the noise schedule to enforce zero terminal SNR; (2) train the model with v prediction; (3) change the sampler to always start from the last timestep; (4) rescale classifier-free guidance to prevent over-exposure. These simple changes ensure the diffusion process is congruent between training and inference and allow the model to generate samples more faithful to the original data distribution.

Diffusion models are often introduced from multiple perspectives, such as VAEs, score matching, or flow matching, accompanied by dense and technically demanding mathematics that can be difficult for beginners to grasp. One classic question is: how does the reverse process invert the forward process to generate data from pure noise? This article systematically organizes the diffusion model from a fresh Langevin perspective, offering a simpler, clearer, and more intuitive answer. We also address the following questions: how can ODE-based and SDE-based diffusion models be unified under a single framework? Why are diffusion models theoretically superior to ordinary VAEs? Why is flow matching not fundamentally simpler than denoising or score matching, but equivalent under maximum-likelihood? We demonstrate that the Langevin perspective offers clear and straightforward answers to these questions, bridging existing interpretations of diffusion models, showing how different formulations can be converted into one another within a common framework, and offering pedagogical value for both learners and experienced researchers seeking deeper intuition.

Diffusion-based generative models' impressive ability to create convincing images has captured global attention. However, their complex internal structures and operations often make them difficult for non-experts to understand. We present Diffusion Explainer, the first interactive visualization tool that explains how Stable Diffusion transforms text prompts into images. Diffusion Explainer tightly integrates a visual overview of Stable Diffusion's complex components with detailed explanations of their underlying operations, enabling users to fluidly transition between multiple levels of abstraction through animations and interactive elements. By comparing the evolutions of image representations guided by two related text prompts over refinement timesteps, users can discover the impact of prompts on image generation. Diffusion Explainer runs locally in users' web browsers without the need for installation or specialized hardware, broadening the public's education access to modern AI techniques. Our open-sourced tool is available at: https://poloclub.github.io/diffusion-explainer/.

A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm.

Multi-agent reinforcement learning in dynamic social dilemmas commonly relies on parameter sharing to enable scalability. We show that in shared-policy Deep Q-Network learning, standard exploration can induce a robust and systematic collapse of cooperation even in environments where fully cooperative equilibria are stable and payoff dominant. Through controlled experiments, we demonstrate that shared DQN converges to stable but persistently low-cooperation regimes. This collapse is not caused by reward misalignment, noise, or insufficient training, but by a representational failure arising from partial observability combined with parameter coupling across heterogeneous agent states. Exploration-driven updates bias the shared representation toward locally dominant defection responses, which then propagate across agents and suppress cooperative learning. We confirm that the failure persists across network sizes, exploration schedules, and payoff structures, and disappears when parameter sharing is removed or when agents maintain independent representations. These results identify a fundamental failure mode of shared-policy MARL and establish structural conditions under which scalable learning architectures can systematically undermine cooperation. Our findings provide concrete guidance for the design of multi-agent learning systems in social and economic environments where collective behavior is critical.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

Originating from the diffusion phenomenon in physics that describes particle movement, the diffusion generative models inherit the characteristics of stochastic random walk in the data space along the denoising trajectory. However, the intrinsic mutual interference among image regions contradicts the need for practical downstream application scenarios where the preservation of low-level pixel information from given conditioning is desired (e.g., customization tasks like personalized generation and inpainting based on a user-provided single image). In this work, we investigate the diffusion (physics) in diffusion (machine learning) properties and propose our Cyclic One-Way Diffusion (COW) method to control the direction of diffusion phenomenon given a pre-trained frozen diffusion model for versatile customization application scenarios, where the low-level pixel information from the conditioning needs to be preserved. Notably, unlike most current methods that incorporate additional conditions by fine-tuning the base text-to-image diffusion model or learning auxiliary networks, our method provides a novel perspective to understand the task needs and is applicable to a wider range of customization scenarios in a learning-free manner. Extensive experiment results show that our proposed COW can achieve more flexible customization based on strict visual conditions in different application settings. Project page: https://wangruoyu02.github.io/cow.github.io/.

Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes. In this work, we identify these approaches as special cases of the Schr\"odinger bridge problem, seeking the most likely stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches.

Effective LLM training depends on predictable scaling of key quantities -- such as final loss and optimal hyperparameters -- with model and dataset size. Qiu et al. (2025) recently showed that this predictability can extend beyond scalars: whole training loss curves can *collapse* onto a universal trajectory after a simple normalization. What remains unclear is whether this phenomenon persists for LLM families trained under *practical scaling recipes*, where width, depth, learning rate, batch size, and weight decay are scaled jointly. We show that it does: loss curves collapse across scales precisely when optimization hyperparameters are set optimally for the given data budget, in accordance with recent empirical scaling laws. Collapse therefore emerges as a signature of compute-efficient training. We demonstrate two applications at scale: (1) deviation-from-collapse provides a sensitive, early diagnostic of training pathologies, and (2) predictability of collapsed curves enables early stopping in large-scale hyperparameter tuning. Finally, we train a competitive LLM family, *Celerity*, using these insights, establishing collapse as an effective tool for developing efficient LLMs.

Diffusion models, as a kind of powerful generative model, have given impressive results on image super-resolution (SR) tasks. However, due to the randomness introduced in the reverse process of diffusion models, the performances of diffusion-based SR models are fluctuating at every time of sampling, especially for samplers with few resampled steps. This inherent randomness of diffusion models results in ineffectiveness and instability, making it challenging for users to guarantee the quality of SR results. However, our work takes this randomness as an opportunity: fully analyzing and leveraging it leads to the construction of an effective plug-and-play sampling method that owns the potential to benefit a series of diffusion-based SR methods. More in detail, we propose to steadily sample high-quality SR images from pre-trained diffusion-based SR models by solving diffusion ordinary differential equations (diffusion ODEs) with optimal boundary conditions (BCs) and analyze the characteristics between the choices of BCs and their corresponding SR results. Our analysis shows the route to obtain an approximately optimal BC via an efficient exploration in the whole space. The quality of SR results sampled by the proposed method with fewer steps outperforms the quality of results sampled by current methods with randomness from the same pre-trained diffusion-based SR model, which means that our sampling method "boosts" current diffusion-based SR models without any additional training.

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called local dimensionality regularization (LDReg). Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.