Denoising

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their statistical efficiency remains limited. Existing theories typically rely on strong regularity assumptions, such as uniformly bounded densities or globally smooth score functions, which fail to capture such intrinsic structures. In this work, we study the sample complexity of diffusion models for learning distributions supported on a union of low-dimensional subspaces. Assuming that the data distribution within each subspace is subgaussian, we show that diffusion models require at most $\widetilde{O}(\varepsilon^{-k \vee 2})$ samples to achieve $\varepsilon$ error in 1-Wasserstein distance, where $k$ is the intrinsic dimension. This near-optimal convergence rate depends only on the intrinsic dimension and significantly improves upon prior theoretical guarantees that suffer from the curse of dimensionality. Notably, our analysis applies to a broad collection of distributions without imposing smoothness, bounded-density, or log-concavity assumptions. Overall, our results show that diffusion models can statistically adapt to intrinsic low-dimensional structure while naturally accommodating multi-modal data, offering a rigorous theoretical justification for their success in complex high-dimensional learning tasks.

Joint audio-video generation aims to synthesize temporally synchronized and semantically coherent visual-acoustic content. However, existing open-source methods mainly rely on either dual-tower designs with posterior alignment or fully unified tri-modal designs that mix textual context, audio and video in one shared space. The former weakens fine-grained audio-video co-evolution, while the latter couples semantic conditioning with low-level synchronization. To address these limitations, we propose NAVA, a Native Audio-Visual Alignment framework for joint audio-video generation. NAVA is built upon context-conditioned native audio-visual alignment: it first establishes audio-video correspondence in a dedicated interaction space, and then uses external context to condition the joint denoising process. Specifically, NAVA is instantiated with an Align-then-Fuse MMDiT architecture, which transitions from modality-aware audio-video alignment to modality-shared joint denoising. Furthermore, we introduce Timbre-in-Context Conditioning to associate reference timbre cues with corresponding speech spans to achieve controllable speech timbre. Experiments on Verse-Bench and Seed-TTS, together with a user study, demonstrate that NAVA achieves superior video quality, precise audio-visual synchronization, competitive audio quality, and stronger reference-timbre controllability using only 6.3B parameters.

Recent advances in reinforcement learning (RL) have achieved great successes by leveraging the multimodality and exploration capability of diffusion policies. Among these approaches, one representative branch focuses on the sampling-based policy optimization. This design enables better exploration capability of the diffusion model, particularly at the beginning of training, but suffer from low exploitation in Q-value information, resulting in a slow policy convergence. Another branch pays attention to gradient-based policy optimization, which sufficiently exploits the gradient of the Q function yet tends to collapse into a unimodal policy with low diversity. To address this issue, we propose CGPO, \textbf{C}ritic-\textbf{G}uided diffusion \textbf{P}olicy \textbf{O}ptimization, which effectively balances exploration and exploitation with the training-free guidance technique integrated into the denoising process of diffusion policy. Concretely, CGPO steers action generation toward high-value regions defined by the critic network and uses the guided actions as regression objectives. In this manner, CGPO reduces the time required to obtain high-quality actions and improves final performance with better balance between the exploration-exploitation tradeoff. We validate the effectiveness of CGPO on 5 MuJoCo locomotion tasks, and CGPO achieves state-of-the-art performance compared with existing diffusion-based RL methods. Notably, CGPO is the first success to incorporate diffusion policy into real-world RL, with its superior performance on Franka robot arm grasping tasks. Our official page is released at https://dingsht.tech/cgpo-webpage.

We present a fully convolutional denoising autoencoder (FC-DAE) for denoising two-time intensity-intensity correlation functions ($C_2$) in X-ray photon correlation spectroscopy (XPCS). Unlike conventional denoising autoencoders that are typically restricted to fixed input sizes, the FC-DAE accepts inputs of arbitrary dimensions while preserving correlation structures across diverse dynamical regimes. The model is trained using experimentally derived $C_2$ data collected at NSLS-II beamlines, with data augmentation applied to expand the diversity of the dataset and reduce overfitting. The FC-DAE successfully recovers intricate dynamical features in low signal-to-noise conditions while maintaining structural fidelity. To assess reconstruction reliability, we employ quantitative metrics to evaluate structural fidelity and identify potential model-induced bias. Our results demonstrate that the FC-DAE provides robust denoising performance with high computational efficiency, enabling recovery of XPCS dynamics under photon-limited and low-dose measurement conditions.

Diffusion models are effective for waypoint prediction in visual navigation, but standard sampling and test time guidance can produce unreliable or inefficient trajectories when updates drift off the training manifold. We propose Fisher Preserving Guidance with Outer Product Span Projection, a training-free inference method that avoids large Fisher drift associated with off-distribution actions while optimizing a task objective. Our method computes the Fisher-preserving update via a low-rank Jacobian factorization, requiring only a single backward pass per step and enabling real-time use. We further introduce Truncated Fisher Denoising Sensitivity as an uncertainty signal and use it for robust multi-sample action blending. Experiments on toy and realistic navigation benchmarks, including Maze2D with TSDF-based guidance, PushT with official Diffusion Policy weights, and visual navigation in simulation and on real robots, demonstrate consistent improvements in performance over strong diffusion-policy baselines without additional training.

Autonomous driving systems are commonly trained and evaluated within limited geographic regions, which hinders their scalability when deployed in new cities. However, significant domain shifts in appearance, road topology, and traffic patterns often cause severe performance degradation under cross-city deployment. Existing approaches based on domain adaptation, data augmentation, or synthetic data generation typically rely on labeled target data, city-specific annotations, or task-specific designs, limiting their scalability and effectiveness for holistic evaluation. In this paper, we introduce CityTransfer-Bench, a geographically disjoint benchmark for evaluating cross-city generalization across perception, segmentation, and planning, and propose CityGen, a diffusion-based generative framework that performs zero-label city adaptation via HD-map-conditioned synthesis guided by city-level visual prompts. Extensive experiments demonstrate that CityGen consistently improves cross-city robustness across multiple tasks, establishing a scalable and label-efficient foundation for generalizable autonomous driving.

We introduce Midpoint Generative Models (MGM), a principled framework for training one-step generative models. MGM is based on a simple symmetry of Flow Matching with linear interpolation: when the two endpoint distributions coincide, the corresponding drift field vanishes at the midpoint time, $t=1/2$. We show that the norm of this field defines a valid discrepancy between distributions, which we call the Midpoint Divergence. We extend this discrepancy beyond the midpoint by introducing randomly flipped interpolations and further generalize it by replacing deterministic linear Flow Matching interpolations with symmetric stochastic interpolants, yielding a generalized Midpoint Divergence. Finally, we derive a variational formulation of our generalized divergence, yielding a tractable objective for training a one-step generator. The resulting MGM algorithm offers an effective and theoretically grounded approach to generative modeling, achieving competitive performance against existing one-step generative modeling methods.

We study minimal attention-only transformers under all-token corruption and show they admit a two-stage empirical Bayes interpretation. A single attention step computes a kernel-weighted posterior mean with respect to the empirical distribution defined by the context. Depth refines this distribution through particle dynamics (Stage 1), while a long-range skip-connection carries the noisy input as a query for posterior inference (Stage 2), revealing distinct statistical roles for depth and attention residuals. The framework isolates a minimal setting in which the context itself induces a depth-dependent energy landscape governing in-context inference. We show that effective denoising can emerge without an explicit noise schedule: a fixed kernel bandwidth and finite integration horizon suffice, yielding a principled depth-noise relationship. We further establish a posterior-mean recovery guarantee for a class of well-behaved priors, where the empirical estimator converges to the Bayes-optimal predictor under asymptotic conditions. Connecting these dynamics to reverse-diffusion limits, our results provide a statistical interpretation of attention as in-context inference via sample-based posterior estimation, without explicit density modeling.

Reliable work zone mapping is important for connected and autonomous vehicles (CAVs) to navigate safely and smoothly through work zone areas. Cone-mounted ultra-wideband (UWB) roadside units (RSU) offer a cost-effective way for work zone layout inference, as roadside anchors and vehicle tags provide direct vehicle-to-infrastructure (V2I) range constraints for work zone geometry reconstruction. However, UWB range estimation is degraded by bursty outliers, non-line-of-sight (NLOS) errors, arbitrary anchor-ordering issues, and vehicle pose uncertainties in practical field deployments. To address these challenges, this study proposes a pose-conditioned, permutation-equivariant predictive denoiser for multi-anchor UWB ranging. The model employs shared anchor-wise temporal prediction to capture range dynamics, symmetric set aggregation to handle unordered and missing anchors, and pose-conditioned residual decoding to incorporate vehicle motion as a geometric prior. A two-stage training strategy first learns prediction from observed ranges, and then fine-tunes the denoiser with NLOS-weighted supervision. The method is evaluated on rare real-world V2I UWB field data collected with a CAV, as well as on controlled large-scale simulation benchmarks for ablative insights. Results show that the proposed method substantially improves range accuracy, cone localization, and work zone geometry reconstruction in challenging NLOS-dominated regimes, remains robust to anchor re-indexing and moderate anchor dropout, and reduces measurement-weighted field MSE by 66.9% relative to the raw input.

Diffusion-based and iterative methods have become effective tools for solving imaging inverse problems. Their reconstruction process naturally forms a trajectory of intermediate estimates. Although these intermediate estimates define a reconstruction trajectory, most methods do not explicitly regularize the transitions between consecutive states. To address this limitation, we introduce TRACE, a training-free TRAjectory-Constrained rEconstruction framework that stabilizes the reconstruction path by coupling adjacent states along the trajectory. This gives a trajectory-level model that can be interpreted as a sequence of proximal updates. Since the exact proximal update is generally intractable, we approximate it with a neural mapping. This yields a diffusion-like reconstruction process with an explicit coupling between neighboring states. We provide a stability analysis showing that temporal coupling bounds trajectory variation and that this control is preserved under untrained network updates. Experiments on linear and nonlinear image reconstruction tasks show that TRACE improves reconstruction quality. Trajectory-level analyses and ablations confirm that temporal coupling directly affects state transitions along the reconstruction path.

Concept erasure has emerged as a promising approach to mitigate undesired or unsafe content in diffusion models, yet existing methods still face significant limitations. While training-based methods are effective, their high computational cost limits scalability. Editing-based methods are more efficient and deployment-friendly, yet they struggle to simultaneously achieve precise concept erasure and preserve overall generative capacity. We identify this core limitation of the editing-based methods as reliance on additive parameter updates. Our empirical analysis reveals that concept semantics primarily depend on neuron direction rather than neuron magnitude, while overall generative capacity relies on the angular geometry of neurons. As additive updates inherently entangle direction, magnitude, and angular geometry, they inevitably introduce unintended interference between concept erasure and overall generation performance. To address this, we propose Orthogonal Concept Erasure (OCE), which reformulates editing-based erasure as multiplicative parameter updates from a geometric perspective. Specifically, OCE applies layer-wise orthogonal transformations derived from a closed-form solution to the parameters, enabling precise concept erasure while preserving the neuron magnitude and angular geometry. Furthermore, to address conflicting constraints in multi-concept erasure, OCE introduces a subspace-level objective with structured subspace manipulation, yielding a more effective and scalable erasure. Extensive experiments on single- and multi-concept erasure demonstrate that OCE outperforms existing methods in concept erasure and non-target preservation, erasing up to 100 concepts in 4.3 s. Code: https://github.com/HansSunY/OCE.

Pretrained foundation models have become an important basis for end-to-end autonomous driving. In contrast to vision-language models pretrained primarily on static image-text pairs, video generative models capture temporal dynamics and motion priors that are naturally suited for driving. We present DriveWAM, a driving world-action model that adapts a pretrained video diffusion transformer into an autoregressive video-action policy. DriveWAM organizes video and action streams into a unified temporal token sequence and trains them under a joint flow-matching objective, preserving the pretrained video-generation architecture while adapting its large-scale video priors to action generation. To incorporate high-level scene understanding, we introduce scene-evolving driving guidance, where a frozen VLM produces chunk-specific semantic intent to guide video-action generation. To keep long-horizon rollout bounded, we further introduce selective KV memory, which maintains bounded modality-aware video and action memory pools through relevance-redundancy cache selection at inference time. Experiments on NAVSIM and the PhysicalAI-Autonomous-Vehicles benchmark show that DriveWAM achieves strong planning performance, and a data-scaling study from 4k to 100k driving clips further confirms the scaling potential of world-action modeling for end-to-end autonomous driving.

Diffusion models have emerged as powerful generative approaches for missing-data imputation, yet most existing methods operate directly in data space and degrade when training data are heavily incomplete. We investigate whether shifting diffusion to a learned latent representation improves robustness under missing-completely-at-random (MCAR) corruption. To this end, we propose a two-stage framework: a robust VAE-based imputer first learns compact semantic features from incomplete observations, and a diffusion model is then trained in the resulting latent space. Across training missing rates, we perform a controlled comparison against pixel-space diffusion models under the same incomplete-data setting. The latent diffusion model maintains high sample quality and remains stable up to 50% missingness, while pixel-space diffusion degrades progressively as missingness increases. For downstream imputation, latent diffusion also achieves consistently better performance than pixel-space diffusion. These findings indicate that latent-space modeling mitigates artifact amplification from zero-imputed inputs and provides a more robust generative prior for incomplete-data learning. Overall, our results support latent diffusion as a strong and practically useful alternative to pixel-space diffusion for missing-data problems.

Reinforcement learning has become a central paradigm for advancing reasoning in large language models, yet most existing methods still depend on stronger teacher models or heavily curated difficult datasets, limiting scalable capability improvement. In this paper, we introduce DenoiseRL, a reinforcement learning framework that substitutes external supervision with recovery-oriented optimization over failures from weak models. Instead of relying on stronger supervision or carefully engineered data, DenoiseRL learns directly from incorrect reasoning traces by converting them into opportunities for improvement, making training more scalable and less dependent on external resources. This yields a richer and more diverse learning signal, improving exploration efficiency from imperfect model behavior. As a result, DenoiseRL improves reasoning performance and overall training efficiency while reducing the need for expensive data curation or stronger teacher models. Empirically, DenoiseRL consistently outperforms strong on-policy RL baselines across competitive mathematical and general reasoning benchmarks and promotes stronger self-corrective behavior as training difficulty increases, highlighting an effective and scalable alternative pathway for improving reasoning in large language models.

Small-molecule drug discovery requires simultaneous optimization of numerous properties of candidate molecules. These properties can be investigated through the analysis of high-dimensional biological signatures, such as cell morphology and transcriptomic perturbations, which provide a rich perspective on the underlying biological mechanisms. However, existing generative methods, which use those signatures for optimization, fail to meet two key requirements: providing precise guidance toward desired phenotypic signatures while maintaining structural proximity to a known hit. We introduce PhAME (Phenotype-Aware Molecular Editing), a latent diffusion framework that overcomes this challenge by recasting molecular optimization as editing in the latent space of a pretrained graph-based VAE. Our central contribution is a compositional classifier-free guidance scheme with two independent scales, one for the phenotype-conditioning and one for similarity to the seed structure, allowing practitioners to control the tradeoff between these two objectives. Empirical evaluations across diverse benchmarks, including docking score optimization and multimodal phenotypic generation, demonstrate that PhAME achieves state-of-the-art results while maintaining high chemical validity and novelty.

The goal of this work is to reduce the effect of photon noise in dental cone-beam CT reconstruction. We consider an inverse problem formulation and develop a databased prior. To this end, we simulate fan-beam acquisitions and add photon noise to the projection data. The prior is obtained by training a gradient-step denoiser using reconstructed simulated acquisitions. The trained model is integrated into a plug-and-play gradient-step algorithm to reconstruct images from simulated projections. Experiments on synthetic data demonstrate the denoising capabilities of the trained model, while qualitative evaluations on real images showcase the algorithm's performance and generalization ability.

Diffusion posterior sampling conditions diffusion priors on measurements, but data-consistency updates are typically scaled by hand-tuned guidance weights and can destabilize sampling under stiff, operator-dependent curvature. We replace scalar guidance with a per-noise-level damped Gauss--Newton correction computed in diffusion-state coordinates. The correction pulls likelihood gradients back through the denoiser, uses a one-sided curvature model that avoids forward denoiser Jacobians, and applies diffusion-calibrated rank-one damping aligned with the denoiser residual. Each correction is solved with matrix-free GMRES using automatic differentiation, and sampling proceeds with a variance-preserving Langevin transition with a closed-form drift/noise split. On FFHQ and ImageNet across inverse problems, it achieves competitive PSNR/SSIM/LPIPS while running markedly faster than most of the compared baselines; on accelerated MRI reconstruction, it achieves the best PSNR/SSIM among the compared baselines.

World Action Models (WAMs) improve robot manipulation by using video-based future representations to condition action generation. In pixel-space WAMs, however, the best action condition is not necessarily the fully denoised video. Controlled denoising-depth scans show that video refinement can reduce action error up to a state-dependent point, after which the gain may saturate or even reverse when late predictions become less action-relevant or physically unreliable. This suggests that action generation should use a state-dependent point along the video noise trajectory rather than a fixed terminal denoising depth. We introduce State-Adaptive Noise Trajectory Scheduler (SANTS), a lightweight scheduler for video-to-action diffusion policies. At each video decision point, SANTS reads the current video-state representation and noise level, then jointly predicts a cumulative stopping hazard and a relative noise-progression ratio. SANTS is post-trained with a path-level reward computed after the frozen action branch generates the final action chunk, so the scheduler is optimized for downstream action quality rather than intermediate video fidelity, while redundant video-state updates are explicitly penalized. Experiments show that SANTS reaches $94.4\%$ overall success on RoboTwin 2.0 and $73.1\%$ average success across seven real-robot tasks, while reducing latency by $81.7\%$ and $79.0\%$ relative to full video denoising, respectively. These results indicate that adaptive selection along the video noise trajectory can preserve the control benefits of WAM-style future reasoning while removing much of its redundant inference cost.

Text-to-image diffusion models generate images through an iterative denoising process, so internal neural layers produce trajectories of activations rather than single static representations. Sparse autoencoders (SAEs) have recently been used to decompose diffusion activations into interpretable feature directions, but most approaches analyze activations at individual timesteps or condition on time rather than learning directly from full activation trajectories. In this work, we introduce residualized temporal SAEs for diffusion activation trajectories. We collect activations across denoising time, fit linear predictors between neighboring timesteps, and represent each trajectory using an initial activation together with residual components not explained by these linear dynamics. Training an SAE on this residualized representation encourages sparse latents to capture structure beyond what is linearly predictable. The residualized decoder directions can be mapped back into activation space, allowing each latent to be analyzed as a feature trajectory over denoising time. Through reconstruction and ablation studies, spatiotemporal feature analysis, and qualitative steering experiments on Stable Diffusion~1.5, we show that residualized temporal SAEs provide a useful framework for studying temporally structured diffusion activations.

Recent advances in large language models have accelerated open-vocabulary EEG-to-imagined-text decoding, where non-invasive neural activity recorded during visual perception is translated into coherent natural language descriptions of viewed stimuli. However, existing systems remain highly vulnerable to biological noise, where corrupted neural projections induce hallucinated or semantically unstable generation in frozen language models. We introduce SYNAPSE (Symbolic Neural Alignment for Precise Semantic Extraction), a lightweight neuro-symbolic framework that stabilizes neural text generation through inference-time symbolic regularization. By purifying EEG-derived semantic candidates using commonsense graph structure and latent exemplars, SYNAPSE improves semantic stability without end-to-end LLM fine-tuning. Experiments across popular EEG decoding benchmarks and multiple frozen LLM backends demonstrate consistent gains over unconstrained prompting baselines, robustness under object-label ablation, and performance commensurate with substantially more resource-intensive fine-tuned systems, while preserving biometric privacy by localizing raw EEG processing entirely within the encoder stack.

Discrete diffusion models have achieved strong empirical performance in text and other symbolic domains, but, especially for uniform-rate models, they often require many steps to generate a single sample. Existing acceleration methods either rely on training additional quantities or suffer from slow mixing. In this work, we propose a novel Gibbs-based corrector for discrete diffusion models, termed Gibbs-Accelerated Discrete Diffusion (GADD). GADD leverages the structure of the concrete score function to construct Gibbs posterior likelihoods directly, without requiring any additional training beyond standard score estimation. We show that GADD achieves an overall sampling complexity of $\mathcal{O}(\mathrm{polylog} (\varepsilon^{-1}))$, yielding the first such rate for diffusion-based samplers for uniform-rate discrete diffusion models. We also conduct numerical experiments demonstrating the practical advantages of GADD across synthetic data, zero-shot text sampling, and zero-shot conditional music generation. These results corroborate the theory and show that GADD consistently improves sample quality and wall-clock efficiency over standard baselines, including vanilla Euler methods and CTMC correctors. Beyond this, our theoretical analysis introduces a novel framework for analyzing predictor-corrector methods in discrete diffusion models, which may be of independent interest. Unlike existing approaches that rely on the Girsanov change-of-measure technique, our method is based on an induction argument that tracks error propagation across predictor iterations while accounting for inaccuracies in the corrector updates.

3D editing is a fundamental capability for scalable 3D content creation. While image editing has rapidly evolved toward large-scale feedforward generative paradigms, 3D AI generation remains dominated by training-free editing pipelines. A central challenge of feedforward 3D editing lies in the lack of high-quality paired supervision. Editable 3D assets require simultaneous preservation of geometry, multi-view consistency, structural coherence, and localized edit controllability. Existing 3D editing datasets often rely on independently generated assets, image-mediated reconstruction or narrow edit taxonomies, leading to inaccurate localization, weak preservation, blurred edit boundaries, and limited semantic consistency. In this work, we introduce a new perspective: scalable feedforward 3D editing should be learned from semantic-part transformations. Based on this insight, we propose Pxform, a high-quality 3D editing dataset with over 100K consistent before/after editing pairs across seven edit types. Instead of treating objects as unstructured shapes, our pipeline grounds edits directly in semantic 3D parts. Built upon Pxform, we further propose PartFlow, a feedforward 3D editing network that injects source-aware latent control into pretrained 3D generative priors. PartFlow introduces mask-aware velocity preservation and render-space consistency supervision to jointly improve edit fidelity and source preservation, while requiring no 3D edit mask during inference. Extensive experiments demonstrate that high-quality semantic-part supervision substantially improves scalable 3D editing, enabling PartFlow to achieve state-of-the-art performance on both geometric and appearance editing benchmarks.

In recent years, financial institutions and firms have increasingly adopted synthetic data to address data scarcity and to generate counterfactual market scenarios. However, reproducing all the statistical properties of financial time series, commonly known as stylized facts, remains an open challenge for many existing general-purpose architectures. In this paper, we present a quality-aware generative framework that combines two classes of generative methods, demonstrating how their integration addresses existing limitations while enhancing the realism of synthetic data. Specifically, we first introduce CoMeTS-GAN (Correlated Multivariate Time Series GAN), a Conditional Generative Adversarial Network (C-GAN) designed to jointly generate mid-price and volume time-series for correlated stocks. We then show how our GAN architecture can be incorporated into state-of-the-art diffusion models to enhance the quality of generated correlation structures. Specifically, the GAN's Critic serves as a quality evaluation module that guides the diffusion process, enforcing learned correlation structures in the generated time-series. Our framework offers a lightweight and responsive solution for realistic stock market simulation, explicitly modeling inter-asset correlation structures. We experimentally validate our framework against leading generative architectures, showing that it more effectively captures the stylized facts of stock markets and models inter-asset correlations.

Flow matching with clean-data prediction has shown that regressing the clean point can exploit low-dimensional structure more effectively than predicting an ambient noised quantity. We ask whether this principle remains useful after images are mapped into a learned latent space, where compression has already removed much of the raw pixel variability. We introduce JLT, a 130M latent diffusion Transformer over frozen FLUX.2 VAE codes, and compare clean-latent prediction with a matched velocity-prediction DiT under the same representation, backbone, and training settings. Although the three variables x, epsilon, and v are linearly convertible for a fixed corruption time, a local Gaussian analysis shows that velocity regression inherits an isotropic target-covariance floor and amplifies low-variance latent directions, while clean prediction damps them. On ImageNet 256 x 256, JLT-B/1 obtains FID-50K 2.50 with classifier-free guidance, with a large matched-target gap over velocity prediction. These results suggest that prediction targets in latent diffusion are representation-dependent geometric choices, rather than interchangeable algebraic parameterizations.

Sampling from learned high-dimensional distributions is a foundational computational problem. We introduce U-turn chains: Markov chains obtained by iterating short forward-backward steps of a diffusion model, in which each step proposes a move that remains on the learned data manifold and, paired with a Metropolis-Hastings correction, samples from energy-modified targets. For synthetic languages, we show that minimal U-turn dynamics undergoes an ergodicity-breaking phase transition driven by fragmentation of the data manifold; ergodicity is restored at larger U-turn magnitude. In the non-ergodic regime, low-level features relax faster than high-level ones, an ordering that inverts only at sufficiently large U-turn magnitude. We test these predictions on natural language and natural images. In both modalities, minimal U-turns relax slowly, especially for high-level features approximated by deep representations in CNNs or LLMs. The layer-ordering inversion appears only at large noise when mixing is efficient -- signatures consistent with strongly constrained, weakly mixing local dynamics. We discuss the implications of these results for sampling with diffusion models.

Learning an energy-based model from data samples is a central problem in machine learning. Many recent and popular methods, such as denoising score matching for training energy-based diffusion models, use stochastic interpolants to corrupt data samples at different noise levels indexed by a time variable. This defines a joint density over both the data space and time, and most methods learn its energy through either spatial or temporal differences. We identify distinct failure modes for both of these approaches. To solve them, we propose Spatiotemporal Noise-Contrastive Estimation (stNCE), a framework for learning the energy through joint spatiotemporal differences. stNCE unifies many existing methods and leads to new training objectives. Experiments on images and molecules demonstrate performance competitive with state-of-the-art density estimation methods.

Diffusion Transformers (DiT) achieve strong performance in image generation but incur substantial inference costs. While prior work has reduced this cost via quantization and distillation, semi-structured sparsity, which can nearly halve FLOPs, remains underexplored. A key reason is that most existing approaches focus on weight sparsification, and pruning 50% of the weights can remove critical model capacity and degrade generation quality. Our study, however, shows that DiT activations are intrinsically sparse and significantly more robust to N:M semi-structured sparsification than weights. Motivated by this observation, we advocate a paradigm shift from weight sparsification to activation sparsification. We propose RT-Lynx, which applies N:M sparsification to activations and incorporates error-compensation techniques to mitigate accuracy loss. We further implement highly optimized CUDA kernels tailored to this setting, achieving up to a 1.55x speedup on average in linear layers. Extensive experiments across multiple diffusion models demonstrate that our method preserves the generation quality of the original models while substantially accelerating inference.

Discrete diffusion models achieve strong performance in text and image generation, but their inference remains slow and must inherently balance sampling efficiency and sample quality. In this work, we present a systematic study of how the \emph{degree of stochasticity} in Markov transitions governs the sampling tradeoff. We show that highly deterministic transitions converge rapidly but suffer from error accumulation, while more stochastic transitions converge more slowly yet can achieve higher final sample quality. Using an information-theoretic analysis, we identify the underlying mechanism as an error-correcting effect induced by \emph{redundant transitions} that symmetrically exchange mass between states, and show that these transitions can provably contract sampling errors. Motivated by this analysis, we propose \emph{Discrete Churn and Restart Sampling} (DCRS), a novel inference algorithm that injects controlled stochasticity by alternating between forward and reverse diffusion processes. Experiments on synthetic datasets and large-scale benchmarks show that DCRS improves the speed-quality tradeoff in the low number of function evaluations regime. On image datasets, DCRS achieves up to a $10\times$ reduction in sampling steps compared to standard samplers while maintaining competitive sample quality, whereas on language benchmarks, we observe more nuanced behavior depending on the corruption process and sampling procedure.

Energetic-materials performance gains translate directly into reduced propellant mass, smaller warheads, and more efficient civilian gas-generators, yet no new HMX-class compound has been disclosed in fifteen years. Designing one is a sparse-label problem: of ~66 k labelled CHNO molecules only ~3 k carry experimental or DFT-quality measurements, and naive generative models trained on the full mixture either memorise the high-performance tail or extrapolate without calibration. We introduce Domain-Gated Latent Diffusion (DGLD): a label-quality gate at training time, multi-task score-model guidance at sample time, and a four-stage chemistry-validation funnel ending in first-principles DFT audit. The result is 12 DFT-confirmed novel leads. The headline compound, 3,4,5-trinitro-1,2-isoxazole (L1), reaches \r{ho}"cal" =2.09 g/cm3 and D"K-J,cal" =8.25 km/s and is structurally dissimilar from all 65 980 training molecules (nearest-neighbour Tanimoto 0.27). A co-headline lead, E1 (4-nitro-1,2,3,5-oxatriazole), exceeds L1 on calibrated detonation velocity (D_"K-J,cal" =9.00 km/s) from a chemotype family disjoint from L1's. DGLD is the only method to land in the productive quadrant (simultaneously novel and on-target) at DFT level. SMILES-LSTM memorises 18.3% of its outputs exactly; SELFIES-GA's best novel candidate loses 3.5 km/s under DFT audit; REINVENT 4 generates novel high-N heterocycles but peaks at D=9.02 km/s. Code, checkpoints, and 918 mined hard negatives are released on Zenodo (DOI 10.5281/zenodo.19821953); the next compound to enter the HMX-class band can be discovered, validated, and recommended for synthesis at the cost of a few GPU-days.

Generative posterior sampling using diffusion models has emerged as a dominant paradigm for solving inverse problems in imaging, which usually consists of three main components: data consistency (DC) guidance, classifier-free guidance (CFG) and stochasticity. While prior arts have focused on how to develop each or all components, less attention has given to how to schedule them, leading to heuristically fixed or partially adjusted suboptimal schedules. In this work, we argue that the interactions among all three components in terms of scheduling are crucial for significantly improved performance in solving inverse problems in imaging. Our analysis shows that aggressive CFG early in sampling conflict with DC guidance, while stochasticity brings the trajectory back to higher-probability regions. Based on these findings, we propose Triadic Dynamics Aware Posterior Sampling (TriPS), which reformulates posterior sampling as a time-varying control problem and optimizes schedules following a triadic trend of decreasing DC and stochasticity scales alongside increasing CFG scale. TriPS achieves this through two strategies: template-based search over functional priors for reliable baseline schedules, and Group Relative Policy Optimization (GRPO)-based reinforcement learning for more flexible temporal curves. Experiments demonstrate TriPS outperforms state-of-the-art baselines in data fidelity and perceptual realism.

We propose OMGTex, an end-to-end diffusion-based framework for reconstructing high-quality and editable facial UV textures from multi-style facial images. Existing texture reconstruction methods face two major limitations: (1) Fragility due to reliance on 3D geometry priors, which are difficult to estimate accurately, especially under facial occlusions or in stylized domains; and (2) A lack of semantic disentanglement, inhibiting region-specific texture editing and style transfer. Our work addresses both challenges simultaneously. Our core innovation is a geometry-free pipeline that directly maps a 2D face image to its corresponding editable UV texture. We introduce two key techniques: First, to address the challenge of UV misalignment common in diffusion generation, we introduce a gradient-guided refinement strategy at inference time, which explicitly corrects structural consistency. Second, we leverage the inherent semantic distribution capability of diffusion models and design a novel training paradigm to enhance this tendency, enabling semantic-aware editing of facial texture. Furthermore, to address the data scarcity in multi-style texture reconstruction, we construct CANVAS, the first comprehensive paired texture reconstruction dataset covering realistic and diverse stylized domains. To the best of our knowledge, OMGTex is the first geometry-free inference framework that achieves robust, style-consistent, and editable facial texture reconstruction across diverse domains. Our method achieves state-of-the-art performance on multiple facial texture benchmarks.

Synthesizing high fidelity contrast enhanced MRI is clinically valuable for safer and more efficient breast cancer screening, yet remains challenging due to complex lesion textures and heterogeneous enhancement patterns.

Current open-source diffusion models struggle to generate stable and synchronized audio-visual content, particularly in scenarios demanding complex semantic reasoning. The root cause is that existing methods rely on coarse text embeddings from off-the-shelf encoders to guide audio-video denoising, which discards fine-grained semantics and, critically, lacks a shared long-horizon plan, leading to uncoordinated denoising trajectories and fragile cross-modal alignment. We propose Baton, the first framework that introduces explicit semantic planning into joint video-audio generation. Our key insight is that complementing coarse text guidance with semantically rich, modality-aware planned tokens, jointly reasoned and mutually aligned before denoising, can simultaneously restore fine-grained semantic detail and establish a shared blueprint that coordinates both audio and video denoising trajectories. Concretely, Baton first introduces the VA-Planner, a multimodal language model equipped with dual semantic alignment towers, where learnable queries cross-attend to both video and audio features to produce a pair of semantically aligned video and audio planned tokens as keyframe-level blueprints. These planned tokens are injected into the diffusion backbone via cross-attention layers, providing temporally grounded guidance complementary to coarse text embeddings. Since planned tokens do not share one-to-one spatial-temporal correspondence with diffusion latents, we further propose Relative Semantic RoPE, a relative positional encoding that maps planned tokens and latents into a shared spatial-temporal coordinate frame, enabling each latent to accurately attend to its positionally corresponding semantic cues. Experiments on benchmarks show the effectiveness of Baton both qualitatively and quantitatively.

Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and unreliable uncertainty quantification. In this paper, we propose Principled Posterior Matching (PPM), a framework that returns to the fundamentals of variational inference, rather than using tricky approximations. Instead of relying on heuristic approximations, we rigorously formulate the exact optimization of the KL divergence via the integration of Fisher divergence. We derive a tractable, equivalent gradient form of this integral, enabling precise optimization without the biases introduced by prior approximations. Our analysis clearly reveals that the mode collapse in previous methods stems directly from this approximation gap. Supported by our theoretical solution, PPM unifies two complementary paradigms: (1) In variational inference, PPM adopts mass-covering divergences that significantly improve the inversion diversity and uncertainty quantification; (2) In amortized inference, it enables the training of an efficient reconstruction network for rapid, single-step reconstruction. Furthermore, our formulation naturally extends to a broader family of divergence measures by generalizing the integral of the Fisher divergence. We validate PPM across challenging computational imaging tasks, including inpainting, super-resolution fluorescent microscopy, and radio interferometric black-hole imaging. In all experiments, PPM achieves superior reconstruction fidelity, faithful multimodal posterior recovery, and well-calibrated uncertainty estimates, establishing a robust framework for scientific imaging.

Sampling-based algorithms for robot path planning offer probabilistic completeness and strong empirical convergence properties across environments with diverse obstacle configurations. However, in practice, these methods often require many iterations to obtain high-quality solutions. This paper proposes Convex-Neural RRT*, an enhanced RRT* variant that incorporates neural guidance to predict informative waypoint regions near high-quality paths. Convex candidate regions are extracted from these predictions, enabling the planner to concentrate exploration on geometrically relevant areas while preserving global exploration. The proposed algorithm is evaluated against Neural RRT*, Neural Informed RRT*, classical RRT*, and LTA* across three environment types and 18 benchmark maps. Experimental results show that Convex-Neural RRT* reduces computation time by 30-75% compared to neural-guided variants and up to 88-98% relative to LTA*, while achieving an average path length reduction of approximately 5% compared to classical RRT*, with larger improvements observed in complex environments. The method also maintains an overall success rate above 99% across varying obstacle densities. These findings indicate that convex-guided neural sampling provides an effective balance between computational efficiency and solution quality, supporting its applicability to time-sensitive robotic navigation tasks.

Diffusion models excel at generating diverse and multimodal trajectories for robotic planning, yet their iterative denoising process introduces latency that is incompatible with high-frequency closed-loop control. To address this problem, we propose Dynamic Neural Koopman Distillation, a framework that distills multistep diffusion inference into a single forward pass while retaining the multimodal expressivity of the teacher model. Specifically, we introduce a Factorized Dynamic Koopman layer that models the denoising process through a factorized latent transition with state-dependent modal gains. We evaluate the proposed method on standard D4RL MuJoCo locomotion benchmarks and a physical Kinova manipulator, comparing against one-step baselines. The results show that our method significantly outperforms existing one-step distillation approaches on the reported locomotion tasks, and reduces the inference latency to the millisecond regime compared with the teacher policy. Hardware experiments further demonstrate that our method enables smooth and fast closed-loop execution while maintaining task success and comparable accuracy. A project page is available at https://fdkoopman.github.io/.

Diffusion Transformers require repeated denoiser evaluations during iterative sampling, making inference computationally expensive. Cache-based acceleration reduces this cost by reusing intermediate representations across denoising steps, but can introduce representation deviations and degrade generation quality. In this paper, we analyze these deviations and show that effective calibration should consider both the direct mismatch caused by reuse and the subsequent trajectory shift induced by earlier corrections. To address this challenge, we propose Trajectory-Consistent Calibration (TCC), a training-free method that calibrates cached representations toward their full-computation counterparts. Specifically, rather than estimating all calibration priors from a single uncorrected cache trajectory, TCC uses an offline iterative procedure so that each prior accounts for the trajectory shift induced by preceding calibrations. Experiments on PixArt-alpha and DiT-XL/2 show that TCC consistently improves FID across representative cache-based acceleration methods while preserving their underlying reuse policies. Notably, in a representative PixArt-alpha cache-acceleration setting based on FORA, TCC reduces FID from 29.83 to 27.35, slightly surpassing the full-computation baseline.

Off-dynamics offline reinforcement learning seeks to learn a target-domain policy from a large source dataset and a limited target dataset under mismatched transition dynamics. Existing approaches such as reward augmentation and data filtering are constrained to the source dataset and cannot synthesize new target behavior to improve coverage beyond the collected source trajectories. While recent model-based methods attempt to address this by learning target-aware dynamics, the generated experience is constructed only at the transition level, which leads to accumulated errors over long horizons. These limitations necessitate a shift toward trajectory-level generation for off-dynamics offline RL. We propose CEDGE, a Cross-domain Energy-guided Diffusion GEneration framework. CEDGE trains a trajectory diffusion model on source-domain trajectories and adapts the generated samples to the target domain through energy guidance. This guidance is derived by minimizing the distribution mismatch between the source and desired target-domain trajectories and is decomposed into return, domain, and behavior energy components. The resulting energy-guided trajectories are useful both for direct planning and as synthetic data for policy learning. Since target adaptation is achieved via energy guidance rather than retraining the diffusion model, CEDGE can be efficiently adapted to new target dynamics compared to previous methods. Experiments on the ODRL benchmark demonstrate that trajectory-level energy-guided generation improves diffusion planning under dynamics shifts and produces synthetic data that improves downstream target policy learning.

Hyperspectral image restoration faces several challenges, including limited training data, strong sensor specificity, and high spectral dimensionality. These limitations hinder the learning of robust hyperspectral priors, motivating the reuse of priors learned from large-scale RGB data. In this work, we propose a minimally trained, lightweight adapter that repurposes frozen pretrained RGB denoisers for hyperspectral restoration through a projection mapping. The method denoises low-dimensional spectral projections and reconstructs the hyperspectral cube through constrained linear aggregation, while preserving plug-and-play compatibility and the stability properties of the underlying RGB denoiser. Experiments on denoising, deblurring, and super-resolution across multiple datasets demonstrate consistent improvements over hyperspectral-specific baselines, showing the strong transferability of large-scale RGB priors.

Minority sampling aims to generate low-density instances on a data manifold and is of central importance in applications such as medical diagnosis, anomaly detection, and creative AI. Existing approaches, however, define minority samples relative to generative priors learned from training data, confining rarity to model-specific notions that may poorly reflect real-world semantics. In this work, we propose a world-centric perspective on minority sampling, which defines rarity with respect to real-world priors rather than generator-induced densities. To this end, we introduce JEPA guidance, a diffusion sampling framework guided by a Joint-Embedding Predictive Architecture (JEPA) -- a class of world models that encode broad, semantically rich representations. JEPA guidance steers diffusion trajectories toward low-density regions under the implicit density induced by the JEPA, thereby aligning generated minorities with real-world semantic rarity. To make JEPA guidance computationally practical, we develop principled approximation strategies accompanied by theoretical error bounds, significantly reducing the overhead of guidance computation. Extensive experiments across unconditional, class-conditional, and text-to-image generation demonstrate that JEPA guidance consistently improves the fidelity and semantic validity of minority samples, outperforming generator-centric baselines in capturing real-world notions of rarity. Code is available at https://github.com/soobin-um/jepa-guidance.

Scattering transforms achieve Lipschitz stability and translation invariance, but dense prediction tasks require preserving spatial structure lost in global averaging. We propose Phase-Aware Scattering Encoder-Decoder, which restores this information by explicitly preserving phase in skip connections. On image denoising (BSD68), breaking translation invariance improves PSNR by $+2.17$~dB; phase preservation adds $+1.03$~dB. A novel spatial shuffling ablation ($-1.26$~dB penalty) demonstrates phase encodes location-dependent structure. We conduct a preliminary extensibility study on a second dense prediction task (ISIC skin lesion segmentation), with full cross-validation as ongoing work. This work advances principled wavelet-deep learning integration, showing how phase information complements scattering's stability-expressiveness trade-off in pixel-level prediction.

Log-likelihood is a standard metric for evaluating generative models. Unfortunately, in contrast to autoregressive models (ARMs), discrete diffusion models generally do not admit exact computation of this quantity. Existing evaluations, therefore, rely on the evidence lower bound (ELBO), leaving unclear how much higher the true value may be. We address this by introducing the Tangent Upper Bound on Evidence (TUBE), a variational upper bound on log-likelihood that admits an unbiased Monte Carlo estimator. Our TUBE extends across latent-variable models, including masked diffusion models (MDMs), any-order ARMs (AO-ARMs), and block variants of both. Applied to block MDMs and block AO-ARMs, TUBE reveals our key empirical finding that these models lie strictly below the exact ARM baseline, showing that ARMs still dominate in likelihood.

Most practical high-resolution text-to-image systems, including latent diffusion and autoregressive models, perform generation in a compact latent space, and a decoder maps the generated latents back to pixels. Yet the latent-to-pixel decoder is reconstruction-oriented, optimized to invert the encoder rather than synthesize more details, and becomes increasingly costly at megapixel scale. This drawback calls for a more expressive and efficient decoding paradigm. Motivated by recent progress in scalable pixel-space diffusion, we introduce PiD, a Pixel diffusion Decoder that reformulates latent decoding as conditional pixel diffusion, unifying decoding and upsampling into one generative module. By denoising directly in high-resolution pixel space, PiD synthesizes $4\times$ and even $8\times$ upscaled images with low latency. For latent conditioning, a lightweight sigma-aware adapter injects noise-corrupted latents into the pixel diffusion backbone, enabling PiD to decode partially denoised latents and terminate the latent diffusion process early. To further improve efficiency, we distill the model using DMD2, reducing inference to just 4 steps. PiD applies to both conventional VAE latents and semantic latents (e.g., SigLIP, DINOv2) used in recent RAE-based models. PiD decodes latents of $512 \times 512$ images into $2048 \times 2048$ pixels in under 1 second with 13 GB peak memory on a consumer RTX 5090, and as fast as 210 ms on a GB200 GPU, about $6\times$ faster than cascaded diffusion-based super-resolution pipelines with better visual fidelity.

We introduce a new approach to high-fidelity 3D scene reconstruction from multi-view RGB images that tightly couples reconstruction with a strong generative 3D prior. We cast scene reconstruction as conditional 3D generation over a set of spatially-localized, overlapping chunks that together tile the scene, scaling generation to large scene extents. Crucially, we inherit the fidelity and completeness of state-of-the-art generative shape models -- we use Trellis.2 as an example -- which we generalize to the scene level. To this end, we propose a projection-based conditioning mechanism that lifts posed multi-view image features into a coherent 3D representation aligned with the generative model, independent of view ordering and spatially anchored to the scene, yielding high-fidelity, multi-view consistent generated geometry. This enables lifting the strong object-level prior of Trellis.2 to multi-view, scene-scale generation, producing faithful, editable PBR mesh reconstructions of indoor environments. As a result, we obtain high-fidelity results that outperform cutting-edge reconstruction methods by 16%.

Robot policy learning benefits from world-action models that capture environment dynamics, but pixel-level prediction entangles dynamics with nuisance factors such as lighting and texture, making learned representations vulnerable to task-irrelevant visual variation. We propose JOPAT, a JOint Pixel-And-Track World-Action Model that predicts latent visual observations, 2D point tracks with visibility, and actions in a single denoising diffusion transformer. The key insight is that tracks provide an explicit representation of motion that captures long-horizon dynamics and remains robust under occlusion or partial out-of-frame motion, offering greater utility than modeling pixel appearance alone. On LIBERO and real-world LeRobot tasks, JOPAT improves over pixel-based baselines, with the largest gains on long-horizon tasks involving occlusion, object interaction, and off-screen motion.

Real-world image super-resolution aims to recover high-quality images from complex and unknown real-world degradations. However, existing generative Real-ISR methods largely inherit the dense latent representations and quadratic-cost global modeling paradigm developed for high-resolution image synthesis, causing computation, memory usage, and inference latency to scale unfavorably with resolution and thus limiting practical deployment. We argue that the key bottleneck lies not in insufficient restoration priors, but in excessive token redundancy and costly token interactions during high-resolution restoration. Motivated by this observation, we revisit Real-ISR from the perspectives of compact latent representation and linear-complexity modeling, and propose SANA-SR, an efficient one-step restoration framework. Specifically, SANA-SR employs a deep compression autoencoder with a 32x compression ratio to drastically reduce latent tokens while preserving restoration-relevant structures and textures. On top of this compact latent space, we introduce a linear-attention DiT with LoRA fine-tuning, enabling efficient high-resolution restoration with linear-complexity token mixing. Extensive experiments on all benchmark datasets demonstrate that SANA-SR achieves highly competitive and often superior quantitative performance against existing methods, while restoring clearer and more realistic textures. Moreover, after pruning, the deployed model runs in 0.019s with 407.95G MACs and 344M parameters, highlighting its strong potential for practical mobile deployment.

Discrete diffusion models have emerged as powerful frameworks for generating structured categorical data. However, efficiently sampling from reward-tilted distributions remains a fundamental challenge. While Twisted Sequential Monte Carlo (SMC) offers asymptotic exactness for this task, estimating the optimal twist function in discrete state spaces necessitates costly Monte Carlo approximations, resulting a severe computational bottleneck at inference. To overcome this limitation, we introduce Contrastive Distribution Matching (CDM), a novel framework that amortizes the cost of SMC inference by learning a parameterized twist function via positive and negative samples. For efficient training, we reformulate the gradient estimator to leverage the closed-form forward kernels of discrete diffusion models. In practice, evaluating our learned twist function incurs less than 5% additional computational overhead compared to a single forward pass of the base model. Through extensive empirical evaluations, we demonstrate that CDM consistently outperforms existing baselines under matched wall-clock time. We validate the effectiveness and versatility of our approach across a diverse range of applications, including toxic text generation, regulatory DNA sequence design, protein designability, and diffusion large language model alignment.

Defocus deblurring in pathological microscopy remains challenging due to the spatially varying and locally discontinuous nature of optical blur induced by a position-dependent integral imaging process. Existing deep learning methods, constrained by shift-invariance assumptions and limited interpretability, are not well suited to such heterogeneous blur patterns. Neural operators provide a principled alternative by modeling defocus formation directly as an integral operator, offering a new perspective on defocus deblurring. However, most existing neural operator architectures for low-level vision rely on globally parameterized kernels that assume smoothness and stationarity, limiting their ability to model heterogeneous and locally discontinuous blur patterns. To address this limitation, we propose the Discontinuous Galerkin Neural Operator (DGNO), which parameterizes the integral kernel using a discontinuous Galerkin formulation with element-local volume operators and interface numerical fluxes. DGNO provides a principled combination of locality, heterogeneity modeling, and global coherence while preserving the underlying physics of optical image formation. Extensive and insightful experiments demonstrate that DGNO surpasses state-of-the-arts, delivering sharper reconstructions, robust handling of spatially varying blur, and scalable high-resolution performance. The code will be released at https://github.com/DeepMed-Lab-ECNU/Single-Image-Deblur.

Generative priors in Image Super-Resolution (SR) often compromise faithful restoration, we attribute this limitation to a fundamental spectral misalignment between isotropic objectives and the intrinsic natural image manifold. While Direct Preference Optimization offers a path to alignment, its reliance on spectrally flat Gaussian noise fails to distinguish authentic high-frequency details from hallucinations. To bridge this geometric gap, we propose ASASR, a theoretically grounded framework that recasts the generative flow into a Sobolev-induced Riemannian geometry by explicitly coloring the noise transition kernel to mirror natural spectral decay. Driving this geometric alignment, we integrate a parametric adversary grounded in the Riesz Representation Theorem, which synthesizes targeted negative samples equivalent to worst-case Sobolev gradients to direct optimization along the tangent space of plausible structural failures. Extensive evaluations demonstrate that ASASR outperforms leading generative baselines, particularly in preserving spectral consistency and structural fidelity, offering a robust solution that effectively mitigates artifacts.

Feature attribution methods promise to identify which input features matter for a model output. In generative language models, however, it is often unclear what should count as a feature in the first place. In autoregressive language models, earlier generated tokens are both outputs of the model and inputs to later predictions. In diffusion language models, generation proceeds through iterative denoising or unmasking rather than fixed left-to-right prediction, so local explanation may target a state of diffusion rather than a next token. We argue that this ambiguity is not merely an implementation detail, but a conceptual limitation of carrying classifier-era feature attribution directly into generative language modeling. We introduce the Attribution Contract, a specification for feature-attribution claims that names what output is being explained, which features are eligible to receive attribution, what generative process is assumed, what is held fixed, and what model score is being attributed. The contract clarifies why the same attribution method can answer different questions depending on how it is instantiated. We argue that many disagreements about feature attribution in generative language models are not disagreements about attribution algorithms, but about unstated explanatory contracts. Using autoregressive and diffusion language models as case studies, we show when attribution to earlier generated tokens, intermediate states, or denoising stages is informative, when it is misleading, and why feature-attribution methods in generative language models should be evaluated as method-contract pairs.

Vision foundation models are widely used as frozen backbones across many downstream tasks, making them a single point of failure under adversarial attack. We study multi-level Floyd-Steinberg error-diffusion dithering as a lightweight, model-agnostic input transformation that disrupts adversarial perturbations while preserving semantic content. Unlike prior work, which was limited to binary dithering, grayscale CIFAR-10, and a single small model trained from scratch, we evaluate across six tasks (classification, segmentation, depth estimation, retrieval, captioning, visual question answering), two model families (DINOv2, PaliGemma), and three attacks of increasing strength (PGD, MI-FGSM, SIA), as well as an adaptive attacker using a straight-through estimator. Our results show that Floyd-Steinberg dithering at intermediate quantization levels, especially when combined with post-processing blur, exceeds or matches all tested baselines, including diffusion-based denoising, with substantially less degradation on clean inputs.

Score matching is an alternative to maximum likelihood estimation when the normalizing constant is unknown or too costly to evaluate. However, vanilla score matching has shown to be inefficient relative to maximum likelihood estimation for multimodal distributions with well-separated modes, which are commonly encountered in practical applications. We compare a novel diffusion-based denoising score matching estimator (DDSME) to the vanilla score matching estimator (SME) in this scenario. In particular, we prove statistical guarantees for both estimators, showing that the error bound for the vanilla SME worsens when the separation between the modes increases, which can be avoided in case of the DDSME with suitable hyperparameter tuning. This provides a novel theoretical explanation for the superior behavior of diffusion-based score matching over the vanilla version.

Representation Autoencoders (RAEs) leverage frozen vision foundation models (VFMs) as tokenizer encoders, providing robust high-level representations that facilitate fast convergence and high-quality generation in latent diffusion models. However, freezing the VFM inherently constrains its spatial reconstruction capacity, limiting fine-grained generation and image editing; in contrast, incorporating reconstruction-oriented signals via fine-tuning disrupts the pretrained semantic space and degrades generative fidelity. To address this trade-off, we propose DecQ, a simple yet effective framework for RAEs. Specifically, DecQ introduces lightweight detail-condensing queries that extract fine-grained information from intermediate VFM features through condenser modules. These queries are incorporated into the decoder to support reconstruction and are jointly generated with patch tokens during generative modeling. By aggregating information from both shallow and deep layers, DecQ effectively mitigates the reconstruction--generation trade-off, improving both reconstruction quality and generative performance. Our experiments demonstrate that: (1) with only 8 additional queries and 3.9% extra computation, DecQ improves reconstruction over the frozen DINOv2-based RAE, increasing PSNR from 19.13 dB to 22.76 dB; and (2) for generative modeling, DecQ achieves 3.3$\times$ faster convergence than RAE, attaining an FID of 1.41 without guidance and 1.05 with guidance.

Discrete diffusion models are often trained through clean-data prediction, but the prediction can be used in different ways to define the reverse dynamics. In Masked Diffusion Models (MDM) these choices largely coincide, whereas in Uniform Diffusion Models (UDM) they do not. We show that the standard plug-in bridge parameterization for UDM is not optimized by the denoising posterior, but by a leave-one-out posterior that predicts each clean token without using its own noisy observation. This identifies a mismatch between the plug-in ELBO and the usual cross-entropy denoising objective. We characterize the leave-one-out target and derive exact conversions between the denoiser, the leave-one-out posterior, and the score. These conversions allow us to disentangle parameterization and training objective. Our results also lead to inference improvements without any additional training through an informed predictor-corrector sampler and improved temperature sampling based on the leave-one-out predictor. We further introduce an absorbing-state reformulation of uniform diffusion that preserves the UDM joint law while decomposing it into masked-diffusion-like sampling operations, with simpler denoising posteriors, carry-over unmasking, and a natural remasking mechanism. On language modeling, leave-one-out parameterizations consistently improve UDM generation, while the absorbing construction matches or surpasses masked diffusion. These results suggest that the empirical gap between masked and uniform diffusion is driven less by the choice of marginals themselves than by parameterization and sampling design. The code and models can be found at https://github.com/samsongourevitch/rev_udm.

A central error measure in Gaussian DDPMs is the path-space KL divergence between the exact reverse chain and the learned Gaussian reverse process. This quantity is especially relevant for procedures such as classifier guidance, which perturb the entire reverse trajectory rather than only the terminal sample. Prior analyses show that standard isotropic reverse covariances suffer an unavoidable $Ω(1/T)$ path-KL error as the number of denoising steps $T$ grows. We show that matching the full posterior covariance breaks this barrier, yielding an order-wise improvement that reduces the path KL to $O(1/T^2)$. To make full covariance matching practical, we introduce the Lanczos Gaussian sampler (LGS), a training-free, matrix-free method for sampling from the optimal reverse covariance using only covariance-vector products, which are available through Jacobian-vector products of the posterior mean. LGS avoids dense covariance storage and auxiliary covariance models. We prove that LGS approximation error decays exponentially in the number of Lanczos steps, where each Lanczos step requires a single Jacobian-vector product. Empirically, using only just three such steps improves sample quality over strong diagonal-covariance baselines, including OCM-DDPM, across standard image benchmarks. This identifies full covariance matching as both theoretically valuable and practically accessible for fast DDPM sampling.

Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential equations, and numerical sampling methods. We write this tutorial to provide a unified and self-contained account of these viewpoints from the perspective of differential equations. Starting from a conditional Gaussian noising process, we derive ordinary differential equation (ODE) and stochastic differential equation (SDE) representations, pass to the corresponding marginal forward dynamics, and then obtain the reverse-time SDE and probability-flow ODE that make generation possible. We show that the central unknown quantity in reverse sampling is the marginal score, explain how score matching becomes the standard denoising objective under a noise-prediction parameterization, and discuss practical reverse-time sampling and guidance. We further place DDPM, DDIM, flow matching, and score-based SDEs in a common framework, and conclude with diffusion language models in continuous embedding space together with a brief discussion of discrete masked-token diffusion. The tutorial is intended as a bridge between the analytical foundations of diffusion processes and the modern generative algorithms built upon them.

Reconstructing continuous physical fields from sparse measurements is a central inverse problem, but data-driven generative models can produce states that violate governing dynamics. We introduce a physics-informed generative solver that separates stable prior learning from inference-time enforcement of conservation laws. Martingale-Regularized Score Matching regularizes score pretraining with a Score Fokker-Planck constraint, yielding a dynamically stable prior. Physics-Informed Implicit Score Sampling then guides denoising trajectories by gradients of physical residuals, projecting samples toward admissible manifolds without retraining. In acoustics, the method co-generates pressure and particle velocity from sparse sensors, enabling dense virtual arrays that suppress spatial aliasing. The same framework generalizes to real-world ERA5 meteorological fields under extreme sparsity. Together, this work establishes a rigorous and generalizable paradigm for solving high-dimensional inverse problems, bridging the gap between generative artificial intelligence and first-principles science.

Identity-conditioned diffusion models enable high-quality and identity-consistent face generation, but they also raise severe privacy concerns, as models may continue to synthesize individuals despite their right to be forgotten. While machine unlearning has been extensively studied for concept and data removal, identity unlearning remains largely unexplored, particularly in models conditioned directly on identity embeddings rather than text prompts. In this work, we study identity unlearning in Arc2Face, a state-of-the-art identity-conditioned latent diffusion model for face generation, and introduce Proximity-guided Identity Unlearning (PIU), an anchor-guided framework for identity unlearning. Specifically, we formulate identity removal as an identity replacement objective that reassigns the source identity to a selected anchor identity in the learned identity space, and we complement it with a proximity-based anchor selection strategy motivated by the geometry of ArcFace representations. We further show that effective unlearning can be achieved through localized fine-tuning of a small subset of identity-sensitive cross-attention layers. Experiments across multiple target identities show that our framework effectively suppresses generation of the target identity while preserving realism and identity consistency for retained identities, as validated by improved performance on unlearning and image-quality metrics, together with qualitative evaluation. The source code for the PIU identity unlearning framework is made publicly available at https://github.com/edgarcancinoe/piu-unlearning.

Whole-body Humanoid-Object Interaction (HOI) is bottlenecked by the scarcity of high-fidelity 3D data. While video generative priors offer a promising alternative, existing methods suffer from \textit{Representation Misalignment} due to their reliance on geometric priors (e.g., explicit CAD models), and \textit{Retargeting Complexity} arising from intensive morphing and morphological mismatch. We propose Imagine2Real, a zero-shot HOI framework for flexible, geometry-free interaction. To resolve misalignment, we formulate robot and object motions as unified 4D point trajectories. To overcome retargeting complexity, our Keypoints Tracker tracks only sparse critical points (base, hands, and object), entirely bypassing the error-amplifying retargeting process. To maintain natural gaits despite these sparse signals, we utilize the latent space of a Behavior Foundation Model (BFM) as the tracker's search domain. Using a progressive training strategy, Imagine2Real learns robust behaviors with simple tracking rewards, enabling zero-shot physical deployment within a motion capture(mocap) system.

Audio context determines which sound components and sources are relevant and which can be perceived as irrelevant (noise) by listeners. For example, traffic noise is informative in urban surveillance but noise for a phone call at the same location. Most current audio denoising systems apply fixed target-noise definitions, often removing useful components in one context while failing to suppress irrelevant components. To address this, we introduce the concept automatic contextual audio denoising (ACAD) which defines target and noise based on the inferred context. In this work, we restrict context to be associated with an acoustic scene class. We label sound events outside the event distribution of a scene class (noise) as out-of-context (OC) and events typical for that scene as in-context (IC). We implement a deep learning method that automatically infers the context of the audio signal and removes OC components, and benchmark it against variants: without context inference, with oracle context, and with separately provided uninformative context. On paired clean/noisy data across diverse contexts, where OC components in one context may be IC in another, our proposed method outperforms other approaches across standard objective metrics, indicating that the model can infer context and context-dependent processing can enhance denoising.