Denoising

Offline multi-objective optimization (Offline MOO) seeks Pareto-optimal designs from static datasets without additional environment interactions. Existing generative methods typically guide sampling with external surrogate or preference models, which adds training complexity and may provide unreliable guidance. We propose ParetoPilot, a plug-and-play method that guides designs to Pareto front at inference time using a pre-trained conditional diffusion model without any surrogate. ParetoPilot introduces an Infer-Perturb-Guide (IPG) engine within the reverse diffusion process. IPG first infers the individual conditional target for each sample in the batch by aligning its conditional and unconditional predictions. It then perturbs these targets collectively across the batch, balancing convergence toward the Pareto front and diversity among samples. Finally, the engine guides the generative trajectory toward the Pareto front by injecting these perturbed targets via standard Classifier-Free Guidance (CFG). Experiments on 51 tasks demonstrate that ParetoPilot achieves the best overall ranking among 16 methods and competitive hypervolume improvement.

Video diffusion transformers have achieved state-of-the-art visual quality, but their high inference cost remains a major bottleneck for real-time applications. Recent distillation frameworks produce autoregressive video diffusion models with reduced latency, yet these models still use a fixed number of denoising steps per frame, wasting computation on predictable frames and under-refining challenging ones. We present DSA, a confidence-guided adaptive computation framework for AR video diffusion. DSA introduces a lightweight confidence head, trained jointly with the generator under a distribution-matching distillation objective, to estimate per-frame denoising reliability. At inference, this confidence signal dynamically adjusts the number of diffusion steps: simple frames terminate early for speed, while complex frames receive additional refinement. Our method requires no extra video data, no heuristics, and little architectural modification. Experiments show that DSA achieves real-time autoregressive video generation, reaching 22.63 FPS with sub-second latency on H100 GPUs, while maintaining competitive or superior VBench quality compared to recent autoregressive and bidirectional video diffusion models. Our results demonstrate that confidence-guided adaptive sampling provides an effective and practical path toward interactive video generation.

Diffusion large language models (dLLMs) generate responses by iteratively unmasking and revising many positions in parallel. This process leaves a rich denoising trace depicting which tokens become confident, which remain unstable, and when commitments form. Existing dLLM reinforcement learning methods use this signal only weakly. Flat rollouts are cheap, but assign a single outcome reward to the whole trajectory. Tree rollouts provide finer, verifiable training signals by branching partial trajectories and propagating leaf rewards upward, but are compute intensive. We ask whether the denoising trace itself can provide tree-like supervision without tree-level compute. We introduce CAPR (Cached-Amortized Path Refinement), a dLLM-RL algorithm that summarizes the denoising trace into a compact path state, uses cached trajectory states to generate cheap sibling continuations, and trains a block-level value head for local block-wise supervision. Under a block-wise unmasking schedule, CAPR records path-state and block-progress features, then redistributes the final outcome reward across blocks according to the tokens revealed in each block. This trains the value head to convert one sparse reward into block-level PPO weights. CAPR therefore recovers much of the granularity of tree search while avoiding full tree expansion, reducing rollout-generation cost to roughly 0.75x that of flat rollouts and 0.6x that of tree rollouts (under standard settings). Across 4x4 Sudoku, Countdown, GSM8K, and Math500, on dense and mixture-of-experts LLaDA backbones, CAPR sets a new state of the art for RL-tuned dLLMs at 256- and 512-token budgets. On Sudoku, it matches the strongest tree-structured baseline at less than one third of the per-step compute.

We consider the problem of generating images whose internal structure -- defined by the distribution of patches across multiple scales -- matches that of a single reference image. Recent approaches address this problem by training a diffusion model on a single image. But even in this setting, training is computationally expensive and requires hours of optimization. Instead, we model the image using a dataset of its patches at different scales. As this dataset is finite and the dimensionality of its patches is small, the score function for a noisy patch can be computed tractably using an optimal, closed-form denoiser, eliminating the need for neural network training. We integrate this patch-based denoiser into an efficient, training-free image diffusion model, and we describe how our method connects to classical patch-based image restoration techniques. Our approach achieves state-of-the-art generation quality and diversity compared to trained single-image diffusion models, and we demonstrate applications, including unconditional image generation, text-guided stylization, image symmetrization, and retargeting. Further, we show that our approach is compatible with latent space diffusion, and we show multiple additional acceleration techniques to achieve megapixel single-image generation in one second, and gigapixel generation in minutes.

Single-image reflection separation is highly challenging under extreme conditions like glare or weak reflections. Existing methods often struggle to recover both layers in glare or weak-reflection scenarios because of insufficient information. This paper presents a diffusion model explicitly fine-tuned for this task, leveraging generative diffusion priors for robust separation. Our method simultaneously generates transmission and reflection layers through a unified diffusion model, incorporating a novel cross-layer self-attention mechanism for better feature disentanglement. We further introduce a disjoint sampling strategy to iteratively reduce interference between the layers during diffusion and a latent optimization step with a learned composition function for improved results in complex real-world scenarios. Extensive experiments demonstrate that our approach surpasses state-of-the-art methods on multiple real-world benchmarks. Project page: https://brian90709.github.io/diff-reflection-separation/

Flow matching models learn to transport samples from a simple prior distribution to a complex data distribution. When prior-data pairs are coupled via optimal transport (OT), the learned trajectories are straight and non-crossing, enabling fast, even single-step, generation. However, computing the OT coupling in high dimensions is intractable, and existing methods attempt to solve the OT problem, at the cost of persistent bias or significant overhead. Rather than solving for the OT coupling, we reformulate the problem. Once the prior is treated as a design choice rather than a fixed input, the OT coupling between prior and data is no longer unique. Many priors admit an OT-optimal identity coupling to the data, leaving us free to choose one that is also tractable to sample. We identify low-frequency projection of natural images as such a choice. The identity coupling between data and its low-frequency representation is empirically OT-optimal, the prior is structured enough to be sampled by a lightweight model at inference, and the remaining flow-matching task reduces to synthesizing high-frequency detail. Interpolating the prior with Gaussian noise further improves generation quality while preserving the OT coupling. The approach requires no modifications to the flow model itself, and integrates naturally with latent-space models, classifier-free guidance, and one-step generation frameworks. Across all benchmarks, our method reduces trajectory curvature by more than $2\times$ compared to existing flow matching methods, yielding better generation quality in the few-step regime.

Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often available too, offering pointwise accuracy without spectral distortion but covering only a small fraction of the domain. We address this by treating NO predictions as auxiliary observations in a diffusion posterior sampling framework. Our method, FreqNO-DPS (https://github.com/niccoloperrone/FreqNO-DPS), combines an unconditional score-based diffusion prior, trained on high-fidelity simulations, with diffusion posterior sampling (DPS) conditioned on sparse observations and guided by a frozen neural operator. Naive integration reintroduces the surrogate's spectral bias; we resolve this with a closed-form, spectrally shaped guidance score that weights the surrogate by its frequency-dependent accuracy and needs no denoiser backpropagation. A distribution-free analysis bounds the approximation error across the frequency-diffusion-time plane and shows the guidance's frequency dependence is preserved regardless of distributional assumptions. On 3D elastic wavefield prediction at 5% and 2% sensor coverage, the method reaches near-zero spectral bias across all bands, where both the surrogate and sensor-only DPS show systematic high-frequency attenuation. Isotropic guidance, the natural baseline, improves pointwise accuracy but carries the bias into the posterior nearly intact, confirming that frequency-dependent calibration is essential, not merely beneficial. The framework needs only paired surrogate/reference data and exploits no problem-specific structure beyond the residual's approximate spectral diagonality, verifiable for new surrogates via the coherence diagnostic we provide.

Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates in isolation, or retain momentum without explaining why it improves empirical performance. Our work bridges this gap by showing momentum in Muon acts as a spectral filter. Under a structured signal-plus-perturbation gradient model, we prove that momentum suppresses perturbations while preserving the dominant signal, thereby enlarging the spectral gap between them. This enlarged gap stabilizes the singular subspaces of the matrix passed to Muon's orthogonalization step, making the resulting update more reliable. We further show that applying momentum before orthogonalization achieves provably stronger alignment with the signal component of the gradient than either reversing this order or simply removing momentum. Experiments across diverse tasks, including LLM pretraining, support our theoretical analysis. More broadly, our theory offers a starting point for understanding the benefits of momentum in other matrix-based optimizers.

Recent world action models leverage video foundation models by aligning broad visual-dynamics priors with executable robot actions. We revisit this alignment from a distributional perspective. Existing formulations typically narrow the aligned prior into an observation-conditioned policy distribution over future actions. In contrast, we keep the distribution broader by modeling the joint space of interaction videos and executable hand trajectories under multiple conditioning regimes. We propose Donk, a unified video-action denoising model for dexterous hands. With language, an initial image, and the initial hand state, Donk samples future videos and bimanual MANO trajectories as an action policy. Without the image condition, the same denoising architecture samples paired video-action rollouts from a text-conditioned distribution, turning the aligned video prior into a data engine. Across action, video, and text-only generation evaluations, Donk improves dexterous trajectory accuracy, preserves strong video fidelity, and produces smooth text-conditioned action rollouts under the same unified training recipe.

Action chunking has become a common inference strategy for flow-based robot policies, improving action coherence by modeling multi-step temporal dependencies in demonstrations. However, the execution horizon is still typically set as an empirical fixed value, overlooking that predictable free-space motions and precision-critical interaction phases often require different replanning frequencies. In this work, we first show that the denoising process of flow-based policies contains an intrinsic signal of task phases: clean-action estimates remain stable during predictable motion phases, but fluctuate more strongly around contact-rich or precision-sensitive operations. Motivated by this observation, we propose DVAC (Denoising-Variance Adaptive Chunking), a test-time method that adaptively determines how many actions to execute from each predicted chunk. DVAC measures the variance of clean-action estimates over the final denoising steps, executes the stable low-variance prefix, and replans before high-variance future actions are committed. To transfer across tasks and rollouts, DVAC further calibrates the threshold with a rolling estimate of the local variance scale. Experiments on LIBERO, RoboTwin, CALVIN, and real-world manipulation show that DVAC improves task success while reducing replanning frequency. With a $π_{0.5}$-based policy, DVAC improves LIBERO success from 94.75% to 98.00% and reduces replanning by 43.0%, while also yielding aggregate gains on RoboTwin and CALVIN and improving real-world execution efficiency.

Latent diffusion models leverage visual tokenizers to compress images into latent spaces for efficient generative modeling. However, better reconstruction quality of a tokenizer does not necessarily translate into better generation quality, suggesting that latent representations should be evaluated not only by fidelity but also by their diffusability. Recent studies have proposed diverse explanations for diffusion-friendly latent spaces, including semantic separability, affine equivariance, distribution uniformity, spatial structure, spectral smoothness, and manifold continuity. Yet these properties are often validated on a limited set of tokenizers, leaving it unclear which factors are most predictive of downstream generation quality and whether such conclusions hold beyond the specific settings in which they are introduced. In this work, we conduct a systematic study of latent diffusability by training a large collection of tokenizers with diverse regularization strategies, architectures, and latent configurations, and evaluating them with multiple downstream diffusion backbones. Our analysis identifies several latent properties that consistently correlate with generation quality and exhibit strong generalization across experimental settings. Beyond existing metrics, we introduce Velocity Irreducible Variance (VIV), a measure of velocity ambiguity induced by trajectory crossings. Extensive experiments show that VIV is one of the most stable predictors of generation quality.

Path planning is essential for Autonomous Mobile Robots (AMRs). Conventional methods for incorporating human preferences into planning typically rely on either complex reward engineering or hardware-intensive solutions. Recent state-of-the-art frameworks leverage imitation learning to train behavior-specific path planning models from expert demonstrations. However, these approaches face two key limitations: limited generalization to unseen environments and low robustness in demonstration collection. To address these challenges, this work introduces an enhanced framework that focuses on two main contributions: an overhauled annotation tool built on ROS 2, and a novel training strategy that integrates diffusion-based augmentation into baseline behavioral cloning models. A dataset of expert demonstrations is provided and evaluated through ablation studies to assess the robustness of the proposed solution. The enhanced approach outperforms state-of-the-art methods with 39.1% lower Absolute Pose Error (APE) and 33.5% lower Fr'echet Inception Distance (FID) while having 93.8% less trainable parameters. Moreover it attains diffusion-level generalization while preserving the real-time, on-edge properties of state-of-the-art models.

We propose a novel diffusion model, Flicker-DDPM, which incorporates flicker (1/f) noise inspired by self-organized criticality (SOC), a widely observed phenomenon in natural systems. Unlike denoising diffusion probabilistic models (DDPMs), which employ isotropic white noise in the forward process, Flicker-DDPM adopts colored noise with power-law spectra to better match the spectral statistics of natural images, whose power spectra typically follow P(k) proportional to 1/k^α. To this end, we develop a colored-noise module based on a spatial correlation kernel, σ(d) = (d + 1)^{-η}, and theoretically establish that adjusting η controls the spectral exponent α of the generated 1/fα noise, enabling adaptation to datasets with diverse spectral characteristics. On CIFAR-10, Flicker DDPM matches or surpasses the generation quality of a standard DDPM baseline using 3.33 times fewer sampling steps, with negligible additional computational cost per step. We further develop a frequency-domain linear theory demonstrating that spectrally matched colored noise linearizes the reverse trajectory, theoretically explaining the observed sampling acceleration.

Score-based diffusion models have emerged as prominent deep generative models; however, their application to tabular data remains challenging because their backbones assume fully specified inputs, whereas real-world tabular data often contain missing values. We propose AugMask, a plug-and-play training framework that adapts missing-unaware backbones to incomplete data by separating conditioning from supervision. AugMask 1) constructs numeric inputs via conditional stochastic augmentation using lightweight auxiliary models, and 2) applies denoising supervision only to observed coordinates. In effect, augmented missing entries serve as uncertain conditioning context rather than training targets. We connect this training rule to a Rao--Blackwellized objective and show that marginalizing missing entries yields a variance-weighted sensitivity penalty, discouraging over-reliance on uncertain completions. Across diverse datasets and missingness regimes, AugMask enables standard diffusion-based tabular generators to outperform specialized missing-aware baselines.

Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise. Low-rankness is itself a useful but limited structural prior, and additional handcrafted priors (e.g., sparsity or smoothness) still fall short of capturing the rich statistics of real-world data. To compensate for this weak inductive bias under heavy corruption, one would like to inject a learned, data-driven prior; however, the state-of-the-art diffusion models are not readily compatible with current TD and tractable posterior inference. To address these challenges, we introduce DiffBCP, a hybrid-prior Bayesian CP decomposition framework that couples a cumulative shrinkage process prior over the CP factors for automatic rank selection with an off-the-shelf pre-trained diffusion model as an implicit data prior on the reconstructed tensor. To make posterior inference tractable despite the coupling among the likelihood, low-rank constraint, and diffusion prior, we develop a split Gibbs sampler: CP factors admit conjugate updates, while the diffusion block is sampled via low-rank-guided denoising. A noise-adaptive coupling schedule further reduces sensitivity to hand-tuned annealing. Experiments on image inpainting and denoising, including high-resolution out-of-distribution images, show consistent gains over Bayesian, nonlinear, and plug-and-play TD baselines.

This paper studies the problem of inverting the DDIM image generation process to recover latent variables, particularly the initial noise map, from a generated image. Existing methods often struggle with accuracy in this task. We propose a novel hybrid approach that combines direct inversion via gradient descent for the first step, followed by a fixed-point method for subsequent steps. Empirical evaluations across three datasets demonstrate that our method significantly improves the prediction of initial latent variables while achieving superior reconstruction accuracy. Additionally, we introduce a new evaluation, called the self-interpolation test, which assesses the quality of images generated from interpolated points between the true and predicted latent maps, offering deeper insights into performance. Our results reveal that while existing methods perform reasonably well in reconstruction, they consistently fail to accurately predict the initial latent variables, resulting in poor performance on the self-interpolation test. In contrast, our method outperforms all others across all metrics, providing valuable insights into diffusion models and enhancing their applications in image generation and editing.

Diffusion models achieve high-fidelity radio map construction through iterative denoising, yet their sampling cost limits practicality in dynamic wireless systems where radio maps must be refreshed repeatedly. Meanwhile, classical propagation models encode valuable scene-level knowledge that standard diffusion inference discards entirely by initializing from pure Gaussian noise. This paper bridges propagation priors and diffusion refinement through a mid-start sampling strategy. A matched propagation prior is perturbed to an intermediate diffusion timestep, and the pretrained diffusion backbone executes only the remaining reverse steps, focusing computation on multipath-aware refinement rather than full reconstruction from noise. We provide theoretical analysis establishing an upper bound on the initialization gap, a sufficient condition under which truncation improves reconstruction fidelity, and a formal characterization of prior-quality sensitivity under aggressive truncation. Experiments on IRT4HighRes show that, at $P_{\text{start}}=0.5$, the proposed method achieves a $2.01\times$ speedup while simultaneously improving NMSE, RMSE, SSIM, and PSNR over the full-step baseline. A prior-quality ablation across three propagation models of different fidelity confirms that reconstruction quality tracks prior quality, with the sensitivity amplified under shorter reverse trajectories, consistent with the theoretical predictions. These results also suggest that mid-start reconstruction quality can serve as a proxy for ranking the scene-level fidelity of different propagation models.

Reward guidance algorithms steer a learned generative process toward the reward-tilted measure at inference time. While empirically powerful, these methods are prone to reward hacking: the guided model over-optimizes the reward at the cost of fidelity to the learned distribution. Prior work has attributed this to the complexity of neural reward functions or implicit biases in diffusion training, but its fundamental origins remain poorly understood. We show that reward hacking arises from an approximation made in most practical implementations of reward-guided diffusion -- finite-particle plug-in estimation of the Doob h-function -- even in the simplest non-trivial settings of Gaussian and Gaussian mixture targets with quadratic rewards. In closed form, we isolate two distinct failure modes of the plug-in estimator: it leads to reward hacking within each mode and it cannot select high-reward modes. We propose a closed-form reward damping schedule that corrects the within-mode bias with no additional compute, and clarify the role of best-of-n sampling in compensating for the mode selection failure. Experiments on Gaussian mixture targets, a 2D checkerboard, and FLUX.1 text-to-image generation confirm that our theoretical insights carry over to practical settings.

Analyzing microstructural defects in transmission electron microscopy (TEM) images, particularly in irradiated metal alloys, is often limited by the availability of high-quality, labeled data. To address this, we introduce a generative data augmentation approach using a mask-conditioned latent diffusion model (LDM) for synthesizing realistic TEM images with controllable, automatically labeled multi-class defect masks. Without requiring manual annotations for generation, our method enables the creation of synthetic image-mask pairs by sampling distributions learned from experimental masks. These generated data were used to augment small experimental datasets of varying sizes (10, 50, and 100 labeled experimental images) to train a Mask Regional Convolutional Neural Network (R-CNN) model for defect detection and classification. Our results show that generative augmentation yields small overall model performance improvements, with up to a 0.02 gain in the harmonic mean of detection and classification F1 scores. However, we also find that the relative contributions to detection and classification improvement depend on the specific train/test data split. These findings highlight the potential of targeted generative models to enhance deep learning performance in data-scarce microscopy-based image quantification tasks.

Despite the remarkable fidelity of generative models, they frequently suffer from mode collapse. Existing strategies for enhancing diversity predominantly focus on intervening during the generation trajectory. We identify a critical oversight that the standard Gaussian initialization often causes trajectories to collapse into dominant modes because it is agnostic to the guidance potential landscape. In this work, we formulate selecting the initial noise from a guidance potential posterior, which effectively re-weights the prior towards diversity-rich regions. To sample from this distribution efficiently, we introduce Diversity-inducing Initialization (DivIn), which leverages Langevin dynamics to actively navigate the initialization landscape, steering initial noise away from collapsing regions while anchoring them to the valid data manifold. Our method serves as an inference-time diversity enhancement compatible with both diffusion and flow matching models. Extensive experiments show that DivIn exhibits a superior performance in both class-to-image and text-to-image scenarios. Furthermore, we highlight that as DivIn is orthogonal to trajectory-based methods, combining them significantly expands the diversity-quality Pareto frontier beyond what either achieves in isolation.

Diffusion-based inverse problem solvers can produce realistic reconstructions, but realism alone does not ensure that the recovered details are supported by the measurement. We study this failure as measurement-conditioned hallucination: visually meaningful content that is either implausible or inconsistent with the measured instance. Our analysis separates Bayes-rule-based diffusion inverse solvers into a prior update and a measurement-conditioning step, showing that hallucinated content can enter through the prior-side proposal before the measurement correction is applied. Motivated by this view, we propose Robust Prior Update (RPU), a solver-level module that probes the local stability of the diffusion prior update, re-anchors the resulting displacement at the current iterate, and leaves the measurement update unchanged. We instantiate RPU in DPS and evaluate it on FFHQ and ImageNet inverse problems using automatic metrics and human faithfulness studies. On FFHQ, RPU improves PSNR and LPIPS over DPS across box inpainting, Gaussian deblurring, and motion deblurring. In human judgments, RPU receives 91.9% of blind non-tie majority preferences and 91.1% of ground-truth-assisted non-tie preferences on FFHQ box inpainting, while the ImageNet Gaussian reader study is tie-heavy but favors RPU among non-tie cases. These results support a targeted claim: robustifying the prior update can improve instance faithfulness in diffusion inverse solvers, especially when the prior shapes weakly constrained content.

Generative models are increasingly used as priors for inverse problems, but their ability to produce realistic images creates a basic trust problem: a plausible reconstruction may be supported by the measurements, or it may be filled in by the prior along unobserved directions. This distinction is especially important in medical imaging, where acquisition operators are designed under scan-time, dose, and calibration constraints. We study generative inverse problems from a measurement-geometry perspective. The central question is whether a fixed measurement operator can distinguish nearby images that are plausible under the generative prior, and whether this relationship can guide better measurements. We introduce a local measurement-manifold compatibility measure that quantifies how well the operator observes prior-relevant tangent directions. Under local regularity assumptions, we prove that this quantity controls the stable part of the reconstruction error, while the generative prior controls off-manifold drift. This worst-direction certificate motivates practical fixed and sequential acquisition rules based on overall local volume preservation, including a posterior-cloud design that adapts measurements at test time without training a sampling policy. Across row-sampling, tomographic, and MR acquisition settings, the proposed scores predict failure modes, explain measurement-induced hallucinations, and guide better sampling. In fastMRI Cartesian sampling, posterior-cloud measurement design improves over strong non-learned ACS-preserving baselines, including variable-density and Poisson-like masks.

Is the uniform-state diffusion framework a more powerful paradigm for discrete diffusion? Recent studies indicate that this may be the case. In combination with predictor-corrector samplers, uniform-state diffusion models (USDMs) produce samples of higher-quality than masked diffusion models (MDMs), and USDMs equal or outperform MDMs in downstream tasks, even though they exhibit greater perplexity. Two issues remain unresolved. First, existing work compares uniform and masked diffusion with un-informed correctors that re-inject noise at random positions, rather than targeting tokens most likely to be wrong. Second, prior work compares full-sequence diffusion models, so we do not know whether the same conclusion holds when tokens are generated block by block. To address these issues, we introduce BlockGen, a blockwise sequence model that we instantiate with both masked and uniform diffusion. BlockGen trains on a mixture of block sizes and its likelihood interpolates between AR and pure diffusion more finely than models with a fixed block size. BlockGen enables AR-informed predictor-corrector sampling (ARPC), which combines AR and diffusion predictions to re-generate unlikely tokens without an auxiliary verifier. Under ancestral sampling, uniform outperforms masked in the block-by-block setting, especially in the few-step regime. Under ARPC, the gap closes and reverses at high NFE. With block size $16$ on GSM8K, MDMs reach slightly higher accuracy than USDMs, and we observe a similar trend in Generative Perplexity on OpenWebText. Find our code at https://github.com/jdeschena/blockgen.

Methods using inertial measurement units (IMUs) provide a wearable alternative to camera-based motion capture. To mitigate drift from inertial signals, recent sparse inertial pose estimators integrate inter-sensor distances measured by ultra-wideband (UWB) ranging. So far, UWB distances have only been used as an additional input feature, ignoring the physical constraints they impose on sensor positions. However, these distances can also be used to reconstruct the underlying 3D sensor layout, which in turn provides more informative input for pose reconstruction. We propose Ultra Diffusion Poser, a diffusion model that explicitly models these geometric constraints. It includes a Spatial Layout Module that analytically reconstructs the 3D sensor positions from UWB measurements. These sensor positions are used alongside IMU signals and UWB distances as a conditioning signal during diffusion. Still, network predictions can violate inter-sensor distance measurements. To address this, we introduce UWB-Diffusion Guidance, which encourages alignment between predicted poses and measured distances during diffusion sampling. Together, these contributions enable our model to achieve state-of-the-art performance, reducing joint position error by up to 22% over prior work.

Image customization learns target subjects from reference concept images and generates conditioned images per text prompts, mainly modifying styles or backgrounds. Prevailing methods adopt fine-tuning to pack diverse concept attributes into a unified latent embedding, yet entangled attributes hinder elimination of irrelevant disturbances from style and background. To address this issue, we propose Equilibrated Diffusion, a frequency-driven approach that disentangles tangled concept features for balanced customization and consistent text-visual matching. Unlike conventional methods learning full concepts with shared embeddings and unified tuning, our work utilizes the inherent link between image frequency components and semantics: low frequencies represent subject content and high frequencies correspond to styles. We decompose concepts in frequency space and optimize each embedding independently. This separate optimization enables the denoiser to capture style detached from subject identity and generalize better to unseen stylistic prompts. Merging multi-frequency embeddings preserves the model's original spatial customization ability. We further deploy mask-guided diffusion to restrict irrelevant background changes and boost text alignment. Residual Reference Attention (RRA) is inserted into spatial attention to retain subject structure and identity consistency. Experiments prove Equilibrated Diffusion exceeds mainstream baselines on subject fidelity and text adherence, verifying our method's superiority.

Parameter estimation in stochastic differential equations is a classical statistical problem of much importance in many scientific fields. Recent work of Tapia Costa et al. (2026) introduced a novel technique for estimating the drift when the diffusion parameter is known, using discrete samples from multiple trajectories. Their method treats drift estimation as a denoising problem, and leverages tools from (conditional) score-matching diffusion models. Although their experiments showed promising results across different drift classes, the question of theoretical guarantees for their estimator was left unanswered. In this note, we address this gap by exploiting techniques from diffusion model theory. More concretely, we derive an explicit risk bound for the time-averaged mean-squared error of said drift estimator. Our bound decomposes the risk into the (i) Euler-Maruyama discretization, (ii) score/denoiser approximation, (iii) noise initialization, and (iv) sampling variance, revealing the trade-offs between the different hyperparameters and sources of error in the estimator.

Recently, novel view synthesis has witnessed remarkable progress, with mainstream methods such as Neural Radiance Fields (NeRF) and 3D Gaussian Splatting (3DGS) delivering impressive results. However, these approaches often struggle to balance rendering speed and model size, and their optimization-based training can be highly time-consuming. Furthermore, they typically rely on dense observations, often failing to produce satisfactory results under sparse-view conditions. Although feed-forward reconstruction significantly reduces the optimization time of 3DGS, its pixel-aligned formulation generates millions of Gaussians from a single image, severely limiting its practical deployment on mobile devices. To address these limitations, we revisit the Multiplane Image(MPI) representation, which represents scenes using a compact set of planar layers for efficient novel view synthesis. Leveraging recent advances in visual foundation models, we utilize predicted point maps for reliable geometric initialization, followed by differentiable optimization. To address the issues of holes and artifacts in sparsely initialized MPI, we introduce one-step diffusion, which participates in both the differentiable optimization of MPI and the postprocessing of rendering results. Compared with a representative GS-based method, our approach is 30.7% faster and uses only 14.8% of its model size, while achieving competitive synthesis quality on front-view scenarios

Diffusion-based dataset distillation has recently emerged as a promising paradigm for condensing large-scale datasets into compact synthetic sets. By leveraging pretrained generative priors, these methods can produce realistic class-conditional samples more efficiently than traditional matching-based approaches. However, most existing diffusion-based methods still adopt a rigid Generate-and-Use'' strategy, where the generated samples are directly treated as the final distilled set under a fixed images-per-class budget. Such a design tightly couples candidate generation with final budget allocation, which may result in redundant waste of the limited budget or insufficiently informative samples. In this paper, we propose Pool-Select-Refine'', a two-stage framework for allocation-aware generative dataset distillation. First, instead of directly using a fixed number of generated samples, we construct an over-complete candidate pool and select a compact subset under the target budget. Second, we refine the selected samples in latent space using soft-label supervision derived from the teacher model, improving semantic alignment while preserving the generative prior. This design explicitly decouples generation, selection, and refinement, enabling more effective use of the distillation budget. Experiments on large-scale and fine-grained image classification benchmarks show that the proposed framework delivers consistent gains over diffusion-based baselines. The results suggest that introducing a curation stage before refinement is a simple yet effective way to improve diffusion-based dataset distillation.

Autoregressive (AR) large language models (LLMs) have achieved broad practical success, but sequential decoding remains a key bottleneck for low-latency deployment. Recent efficient-inference work has progressed along two axes: reducing the cost of each model invocation through efficient architectures, and reducing serial decoding steps through parallel generation. Hybrid attention backbones address the former, while diffusion language models (dLLMs) pursue the latter via iterative parallel denoising. Combining these advantages remains challenging: AR-to-dLLM conversion often fails to preserve seed-checkpoint capability, and hybrid-attention recurrent states and masking constraints make diffusion training and serving nontrivial. We present FLARE, a systematic conversion framework for hybrid-attention LLMs. Our analysis identifies transfer data quality as the primary determinant of capability preservation, outweighing loss formulation and attention-mask design. The resulting framework combines a token-equal AR-and-diffusion objective, hardware-aware kernels, and unified inference, enabling one checkpoint to support both AR-style verified decoding and diffusion-style parallel denoising. Starting from strong AR checkpoints with limited post-training data, FLARE is competitive with leading open-source dLLMs across model scales and delivers consistent throughput gains over open-source dLLM baselines in single-GPU concurrent serving. Our results further suggest that practical dLLMs are limited not only by decoding algorithms, but also by transfer data quality and the training inefficiency of current block-diffusion objectives, motivating joint design of data, objectives, architectures, and inference systems.

Diffusion models have emerged as a leading framework for deep generative modeling. While the standard Gaussian formulation is theoretically convenient, its suitability for heavy-tailed datasets remains unclear. To address this, heavy-tailed diffusion models (HTDMs) extend the standard formulation by replacing the Gaussian distribution with a Student's t-distribution, thereby improving tail fidelity on heavy-tailed datasets. Although stochastic differential equation (SDE)-based sampling is possible in HTDMs, it has not been fully explored. In this paper, we propose an SDE-based sampler for HTDMs that explicitly incorporates a state-dependent diffusion coefficient. This state dependence naturally induces a self-regulating annealing mechanism by adaptively modulating the effective noise scale. We theoretically explore this mechanism and experimentally verify its necessity for reproducing samples from a heavy-tailed distribution.

Generating realistic time series is essential for scientific research and real-world applications. However, existing methods often emphasize overall distributional fidelity while failing to faithfully capture extreme events. To advance existing research, we propose E4GEN, an explainable diffusion framework for extreme event-aware time-series generation. E4GEN provides systematic insights into when, what, and how to control extreme-event generation through three key components. First, E-Activator learns the dataset-adaptive extreme-control signal activation step during the denoising process without interfering with regular temporal components, including trend and seasonality. Second, E-Predictor determines what control signal to enforce through Self-Driven Semantic Prediction, where each sample derives its own control signal by inferring latent extreme-event information during generation. It also includes a novel Data-Conditioned Training, Noise-Initiated Sampling mechanism to address the issue of unavailable training labels. Third, E-Control specifies how to control extreme-event generation through a trainable Extreme Control Network, which transforms the semantic control signal into layer-wise signals and injects it into the denoising process. We evaluate E4GEN on six datasets with 17 metrics, and extensive experiments show that E4GEN outperforms state-of-the-art models across multiple dimensions, including overall fidelity, extreme-event fidelity, and downstream utility.

Bayesian inference provides a principled framework for modeling epistemic uncertainty in neural networks by treating predictions as distributions rather than deterministic values. Meanwhile, diffusion-based models for 3D molecular graph generation operate on fragile geometric structures governed by strict chemical constraints, making inference highly sensitive to uncertainty miscalibration. A largely overlooked issue is that epistemic uncertainty arising from the learned denoiser interacts with the aleatoric uncertainty intentionally injected during reverse diffusion, leading to systematic variance inflation and a mismatch between the true distribution and the simulated distribution. This effect is particularly detrimental for high-precision molecular generation, where even small deviations can violate chemical validity. In this work, we provide a theoretical and empirical analysis of how epistemic uncertainty propagates through diffusion inference and degrades sampling quality. Building on this investigation, we propose UCD (Uncertainty-Calibrated Diffusion), a simple yet effective method that calibrates the reverse diffusion process to account for epistemic uncertainty. Extensive experiments on standard 3D molecular benchmarks demonstrate that UCD consistently improves sampling quality across diverse baseline methods, establishing new state-of-the-art performance for 3D molecular diffusion. The code is available at https://github.com/jiuguaiwf/UCD.

Reconstructing a photorealistic 3D face avatar from a single unconstrained photograph is challenging: feed-forward 3D Gaussian Splatting (3DGS) models degrade on out-of-distribution inputs, while pretrained diffusion models produce high-fidelity images but lack multi-view consistency. We observe that these paradigms are fundamentally complementary: explicit 3D representations guarantee geometric consistency, whereas 2D diffusion priors ensure photorealism. Building on this, we propose SplatShot, a training-free framework that couples these representations directly within the denoising process. Given a base 3DGS face model and a single reference image, we jointly denoise all target views using a per-step 3D feedback loop. At each timestep, we predict clean images from the noisy latents, refit the 3DGS to these multi-view predictions, and back-propagate the photometric discrepancy between the 3DGS re-renderings and 2D predictions into the noise estimate. This steers the sampling trajectory toward strictly 3D-coherent, identity-faithful outputs. Experiments on diverse in-the-wild images demonstrate that SplatShot produces 3D avatars with superior identity preservation, photorealism, and multi-view consistency.

Aspect-Based Sentiment Analysis (ABSA) encompasses seven distinct subtasks, each focusing on different extracted elements. Despite the proven success of generative models in unified aspect sentiment analysis, existing approaches often rely on auto-regressive token-by-token generation without grasping the whole information of the aspect and opinion terms, resulting in boundary insensitivity, particularly in context of multi-word aspect and opinion terms. To address these issues, we present DiffuSent, a non-auto-regressive diffusion framework that systematically formulates all ABSA subtasks as boundary denoising diffusion processes, progressively refining boundaries over noisy states. Furthermore, we introduce a contrastive denoising training strategy which effectively address duplicate predictions with subtle variations introduced by diffusion process. Extensive experiments across 28 settings (7 subtasks x 4 datasets) demonstrate that DiffuSent achieves delivers consistent improvements over the strongest generative and span-based systems. DiffuSent exhibits notable gains on multi-word triplets, achieving an average improvement of +2.48 F1, and maintains robust extraction accuracy in sentences containing multiple sentiment triplets. Moreover, the non-auto-regressive decoding enables substantial efficiency benefits, reaching up to 181 times faster inference than auto-regressive generative baselines

Text-to-Image (TTI) systems are now everyday infrastructure for journalism, education, advertising, and public communication, and the demographic and cultural stereotypes they inherit from training data (rendering women, people of colour, older adults, and non-Western cultures as under-represented or caricatured) become a population-level harm at deployment scale. Existing mitigations either require costly retraining, infeasible for the closed-source backbones that dominate consumer products, or rely on fixed demographic templates that ignore cultural context. We present KG-FairDiff, a model-agnostic, inference-time framework that formalises fairness-aware prompt refinement as a constrained optimisation problem and operationalises it as a closed-loop pipeline: a knowledge graph of ~1,200 culture- and bias-related triples retrieves structured context, an LLM rewriter proposes refinements, and a validator accepts only prompts that reduce a divergence-based fairness loss while preserving semantic fidelity to the user's original intent. We prove a finite-termination bound for the refinement loop, contribute a mathematically consistent evaluation suite linking Bias-P/Bias-W to divergence from target distributions and ENS to KL divergence, and audit eight widely-deployed backbone generators. KG-FairDiff substantially reduces gender, race, age, and intersectional disparities while preserving prompt semantics, offering a practical, deployment-ready route to more equitable generative AI.

We address text-based 3D human motion editing, where the goal is to preserve the style and structure of a source motion while applying edits described in natural language. The release of the MotionFix dataset has spurred active research into training-based diffusion models that directly generate an edited motion from a source motion and a text instruction. While previous works have focused primarily on learning when an edit should occur temporally, our goal is to create a model that understands not only this temporal aspect but also which specific joints are responsible for the change. Targeting this, we propose a novel architecture and a complementary auxiliary task to aid its training. Our architecture consists of two axis-anchored transformers, which extract distinct features along the joint and time dimensions respectively, and a cross-axis fusion block that integrates these representations. We further introduce an auxiliary task that trains the joint-anchored transformer to regress the Soft-DTW distance between source and target joint rotations. This objective teaches the module to understand which joints to modify and which to preserve. Through comprehensive experiments on the MotionFix dataset, we demonstrate that our method significantly improves semantic alignment with both the text instruction and the source motion, as well as the overall fidelity of the generated motion, achieving state-of-the-art results.

Coordinating multiple robots in shared environments requires generating feasible trajectories for each agent while accounting for interactions among agents. Centralized planning approaches become difficult to scale as the number of robots increases, while decentralized approaches that allow each agent to plan independently do not inherently account for inter-agent interactions. This paper presents a framework for coordinated multi-robot motion planning that combines decentralized generative trajectory planning with multi-agent reinforcement learning (MARL)-based coordination. Each robot independently generates candidate trajectories using a diffusion model trained on single-agent motion data, leveraging the generative model's ability to produce feasible and diverse trajectories. To reduce conflicts between agents, a centralized value function trained via MARL guides the reverse diffusion process through gradient-based steering, enabling interaction-aware trajectory generation without centralized joint planning or retraining of the generative model. This guidance follows an exponential tilting formulation, in which the value function biases the denoising distribution toward trajectories with higher expected multi-agent return. The framework is evaluated in a simulated maze environment with four mobile robots. Experimental results show that the proposed value-guided diffusion planning reduces the inter-agent interference rate from 55.4% to 41.8%, demonstrating that coordination can be effectively achieved while preserving the scalability of decentralized trajectory generation. These results suggest that MARL-based value guidance can effectively introduce coordination into decentralized generative planners without requiring a fully joint multi-robot model.

Reconstructing the three-dimensional distribution of dark matter from weak-lensing observations is a central but highly ill-posed inverse problem in cosmology. Unlike standard 3D reconstruction with multiple viewpoints, we observe the universe from a single line of sight, through noisy shape distortions of galaxies with uncertain distances, so meaningful recovery of the 3D matter field requires strong prior assumptions. Existing methods either produce point estimates with handcrafted priors or use neural ensembles for approximate Bayesian uncertainty, and struggle to capture the non-Gaussian, filamentary structure of the cosmic web. With the advent of new high-resolution cosmological simulations, we now have an alternative source of prior knowledge that captures the nonlinear statistics of structure formation with far greater fidelity than analytic prescriptions. We leverage these simulations to build a new dataset $\texttt{Conicus3D}$, which enables us to learn a data-driven diffusion-model prior capturing the full 3D distribution of dark matter structure across cosmic time. Building on recent plug-and-play approaches, we modify a diffusion-based posterior sampling scheme to the 3D weak-lensing setting, combining the learned prior with a differentiable physical forward model. On realistic simulations targeting a modern weak lensing survey, our approach yields substantially improved 2D and 3D reconstruction accuracy over baseline methods. Moreover, it produces posterior samples whose statistics closely track the underlying simulations, while remaining robust to moderate shifts in cosmology.

Parameter compression of class-conditional diffusion models reveals an underexplored limitation in output-level distillation: the unconditional score branch remains unsupervised, leaving the classifier-free guidance gap underdetermined in the student. This gap, amplified at every denoising step, admits degenerate solutions where both branches collapse toward identical predictions, rendering guidance ineffective despite low output-level training loss. This paper introduces DASH, a dual-branch distillation framework that independently supervises both score branches, uniquely specifying target branch outputs for each training sample through independent branch constraints, with an anchor term regularising conditional predictions toward ground-truth noise. The framework further introduces TIRT Transfer, which copies the teacher's converged per-timestep importance curriculum into the student as a frozen prior, eliminating the need to relearn it within limited distillation budgets. Experiments on CIFAR-10 and CIFAR-100 demonstrate that 5.9x compression maintains quality within 4 FID points of the teacher at 50-step DDIM sampling, considerably outperforming training from scratch with guidance fidelity well preserved. Ablation studies confirm that unconditional supervision is the dominant contribution, accounting for over 60% of total distillation gain. Curriculum transfer and anchor regularisation provide complementary benefit, together validating dual-branch constraints as empirically essential for guidance-preserving compression.

Fast and accurate prediction of crystal properties is a central challenge in new materials design. Graph neural networks and Transformer-based models have emerged as powerful tools for this task due to their ability to encode the local structural environment of atoms within a crystal. However, these models are data-hungry, and in practice, labeled data for crystal properties are scarce. Pretraining-finetuning strategies, particularly those based on diffusion models, have shown promise in addressing these limitations. In this work, we introduce a novel latent diffusion based pretraining framework, CrysLDNet, designed to mitigate data scarcity. Our approach integrates a Variational Autoencoder (VAE) with a diffusion model during the pretraining stage. The VAE encoder maps 3D crystal structures into a smooth latent space within which the diffusion process is applied. This latent diffusion pretraining enables the graph encoder to effectively capture structural and chemical semantics from large-scale unlabeled data, which can then be finetuned for specific property prediction tasks. Comprehensive experiments on popular DFT datasets for property prediction reveal that CrysLDNet significantly outperforms both training-from-scratch and pretrained baselines, with improvements of 4.26% and 4.90% on the JARVIS and MP datasets, respectively. Additionally, the learned representations remain robust in sparse-data conditions and are expressive enough to correct DFT errors when finetuned with limited experimental data. Code is available at: https://github.com/shrimonmuke0202/CrysLDNet.git.

Multimodal MRI provides complementary information for neuroimaging analysis, where different imaging modalities capture distinct anatomical, tissue, and pathological features that support the development and evaluation of downstream AI applications. Although large-scale structural MRI resources are increasingly available, their modality coverage is often uneven across public and pooled neuroimaging datasets. This uneven modality coverage is further complicated by heterogeneity across sites, scanners, and acquisition protocols, as well as demographic and clinical variables that are often sparse, inconsistently recorded, or unavailable across studies. Synthetic MRI generation can help address this imbalance by synthesizing target-modality volumes for dataset augmentation and controlled synthetic cohort creation. However, many existing MRI synthesis approaches are trained on narrow modality sets or relatively homogeneous cohorts, limiting their applicability to large pooled neuroimaging resources where modality availability, acquisition protocols, and metadata coverage vary substantially across datasets. Diffusion models have become an attractive approach for MRI synthesis because of their strong sample fidelity and diversity, but sampling directly in 3D voxel space is computationally expensive and slow at inference. Latent diffusion improves practicality by synthesizing MRI in a learned, 3D latent space, although generation quality depends on the autoencoder's reconstruction fidelity and the resulting latent distribution. Our approach combines a Wavelet-Fusion variational autoencoder (WF-VAE) latent compressor with a conditional 3D U-Net diffusion model trained in the learned latent space using explicit modality and metadata conditioning. Our proposed Wavelet-Fusion Diffusion Model (WFDM) achieved the strongest distributional alignment among the evaluated synthetic MRI generators.

Diffusion models have emerged as the backbone of modern generative AI, powering advances in vision, language, audio and other modalities. Despite their success, they suffer from hallucinations, implausible samples that lie outside the support of true data distribution, which degrade reliability and trust. In this work, we first empirically confirm previously proposed hypothesis that score smoothness causes hallucinations in Image Generation diffusion models and provide a density-based perspective. We further formalize this notion by linking the hallucinations probability mass to lipschitz constant of the learned score function. Motivated by this, we introduce a Variance-Guided Score Modulation (VSM) strategy that controls the score Jacobian, in turn reducing score smoothness and better approximating the ground truth score that decreases hallucinations. Empirical results on synthetic and real-world datasets demonstrate that our approach reduces hallucinations (up to ~25%) while maintaining high fidelity and diversity, providing a principled step toward more reliable diffusion-based image generation. We also propose two benchmark datasets with extreme semantic variation for systematic hallucination evaluation. Code and Datasets are publicly available at https://github.com/bhosalems/VSM.

We propose Parameterized Diffusion Policy (PDP), a framework for learning diffusion policies conditioned on low-dimensional, continuous parameters embedded in a learned behavior manifold. By constructing this manifold so that distances between latent representations reflect the semantic similarity between physical trajectories, we transform diffusion from a mechanism for stochastic diversity into a precise and optimizable tool for behavior steering. Our approach enables smooth interpolation between known strategies and efficient adaptation to novel constraints without updating policy weights. We demonstrate that PDP significantly improves adaptation performance on complex multimodal benchmarks in both simulated and real-robot experiments compared to standard diffusion policies, particularly in scenarios requiring the synthesis of novel behaviors.

This letter studies CSI denoising for MIMO--OFDM with variable NR resource block (RB) allocations. ReFLEX is a length-generalizable Transformer whose frequency attention uses a relative-frequency position bias (RFPB) generated from subcarrier offsets. A single checkpoint handles unseen RB lengths and can be applied to sparse DM-RS observations in the tested RB5/RB10 PUSCH setup without retraining. In a 3GPPTR38.901 UMa NLOS channel, ReFLEX achieves about $-9.6$dB NMSE on unseen RB lengths. In NR PUSCH/UL-SCH simulations, ReFLEX denoising followed by time-frequency interpolation reduces the 10% BLER threshold by about 2--3dB.

Diffusion models have shown promising performance as data-driven priors for computational imaging, as well as some capacity to detect out-of-distribution (OOD) images. However, existing approaches to OOD detection often require some knowledge of the shifted distribution, fail to detect subtle or localized distribution shifts, and operate on full images, rather than the indirect measurements available in inverse problems. We propose an OOD detection metric based on the Kullback-Leibler divergence between the diffusion prior and the posterior distribution, that (i) does not require any calibration data or knowledge of the shifted distribution, and (ii) can detect whole images as OOD as well as localize OOD patches within an image. Experimentally, we show that this metric can detect subtle yet semantically meaningful distribution shifts, such as the shift from healthy liver CT scans to those with tumors, and generalizes across different types of diffusion models, datasets, and inverse problems. Our code can be found at https://github.com/voilalab/KLIP.

Text-to-video (T2V) generation faces challenging questions when generating videos with long horizons containing multiple events. Inspired by the intrinsics of the diffusion process, we probe video diffusion transformers (DiTs) and uncover intrinsic turning points in the DiT denoising trajectory where conditioning text affects generation from global layout to fine-grained details. Building on this finding, we present TunerDiT, a simple yet effective progressive steering method that requires no additional training for multi-event generation. TunerDiT comprises two steering handles: (1) Event-Partitioned Masking that enforces event boundaries while allowing cross-event transition bands; (2) Cross-Event Prompt Fusion that injects neighboring event semantics for late-stage refinement. We contribute a self-curated prompt suite for benchmarking multi-event generation, i.e., Meve. TunerDiT achieves state-of-the-art performance across 8 metrics and offers a tunable trade-off between video consistency and event separation, compared with other training-free methods. The improvement in text alignment increases with the event count, indicating a scaling possibility with increasing event count.

We present UNISON, a latent diffusion framework that unifies speech generation, sound generation, and audio editing within a single model. A single model handles text-to-audio, text-to-speech, zero-shot speaker cloning, mixed speech-and-sound generation, scene-level audio editing, speech-in-scene editing, and timed temporal composition, all of which share a single set of weights. Our architecture features two core designs: (1) Layer-wise deep LLM fusion, which injects hidden states from uniformly sampled layers of a frozen MLLM into corresponding MM-DiT blocks via learned projections, providing depth-matched semantic conditioning that improves instruction following over single-layer baselines; and (2) a unified multi-task architecture where task identity is encoded solely by a channel-wise mask and source audio is provided through VAE-encoded channel concatenation. Training is stabilized by an online GPU-side multi-task data synthesis pipeline with task-homogeneous batching and a two-stage curriculum. With 621M--732M trainable parameters, UNISON achieves results competitive with or exceeding task-specialist models across evaluated domains, while being roughly $4\times$ smaller than comparable unified systems.

Masked Generative Models (MGMs) enable parallel decoding and achieve strong performance across modalities, but require full-sequence bidirectional transformers at every step, making training costly and degrading quality under low sampling budgets. Existing work improves efficiency via better samplers or cheaper fixed-depth denoisers, but they still allocate a fixed amount of denoiser computation to each refinement step. We introduce Fixed-Point Masked Generative Models (FP-MGMs), which replace part of the denoiser with a fixed-point solver over shared attention layers to enable adaptive depth with fewer parameters. To make it more effective for masked generation, we first introduce a cross-step consistency loss, which aligns hidden representations at neighboring denoising steps and, second, three-state reuse (3SR) which warm-starts the solver using the previous solution by treating differently unchanged, still-masked, and newly revealed tokens respectively. Together, these components define our complete training-to-inference framework for fixed-point masked generation, \emph{CoFRe}. We also show that pre-trained MGMs can be converted into FP-MGMs with short fine-tuning, avoiding full retraining. Across modalities, CoFRe improves the quality and cost trade-off. On OpenWebText, CoFRe reduces parameters by 38.8%, training time by 11.5%, and VRAM by 16.9%, while improving generative perplexity from 830.8 to 101.8 at a budget of $96$ transformer-block forward passes, compared to MDLM. In ImageNette, CoFRe reduces training time by 48.6% and VRAM by 50.7%, while improving FID in all sample budgets tested. Overall, CoFRe offers a practical framework for cheaper training and stronger low-budget masked generation.

Riemannian diffusion models generalize score-based generative modeling to manifold-supported data via stochastic diffusion equations on the manifold. However, training requires sampling from and differentiating the manifold heat kernel, which is rarely available in closed form beyond a few highly symmetric manifolds. We propose a general approach that approximates the heat kernel by directly solving the manifold heat equation with a physics-informed neural network (PINN). Given an explicit manifold specification, we choose a coordinate system, derive the corresponding heat (Fokker--Planck) equation and a short-time asymptotic approximation, and then train a PINN to learn the log heat kernel. The resulting surrogate enables both forward noising (heat-kernel sampling) and conditional-score evaluation for denoising score matching. We demonstrate the method on diverse manifolds including $S^2$, $SO(3)$, $\mathrm{SPD}(n)$, and permutation-quotiented point clouds.

Ordinal Regression (OR) aims to predict target values with inherent order, underpinning critical applications across diverse domains, from recommender systems to computer vision. Though having evolved from naive regression to discretization-based classification and generation, existing paradigms remain fundamentally constrained by quantization artifacts and the lack of global ordinal topological perception. These methods typically enforce rigid boundary delineations, failing to capture the non-stationary semantic transitions inherent to ordinal data. In this paper, we propose a novel paradigm where OR is formulated as a Continuous Generative Ordinal Regression task. Under the novel paradigm, we introduce DiffOR, a unified framework that leverages diffusion models to recover continuous ordinal values via iterative denoising, thereby enabling the dynamic learning of soft semantic transitions. To explicitly preserve ordinal topology, we devise a Dual-Decoupling Strategy: Spatially, Multi-scale Increment Aggregation decomposes targets into hierarchical continuous increments; Temporally, Dynamic Denoising Perception synchronizes denoising steps with feature frequencies, ensuring robust coarse-to-fine refinement. Theoretically, we show that the proposed method can significantly enhance both representation capability and mechanistic interpretability. Extensive experiments on 12 benchmarks across four domains validate DiffOR's consistent superiority over state-of-the-art methods, establishing a new standard that demonstrates strong potential as a general-purpose solution for universal ordinal regression.

Cross-modal 2D-3D gait recognition is impeded by inherent domain discrepancies between 2D silhouette and 3D LiDAR range-view representations. While prior methods align only final embeddings, we propose DiffCrossGait, which reformulates cross-modal matching as trajectory-level alignment in an identity-relevant latent diffusion space, rather than assuming full equivalence between 2D and 3D observations. By driving both modalities with shared Gaussian noise within a latent space, we enable continuous alignment throughout the generative evolution. We introduce a Tri-Phase Alignment Strategy that exploits varying noise intensities to enforce identity anchoring, dynamics consistency, and cross-modal structural recoverability, thereby constraining both modalities to share denoising dynamics and bottleneck structure, which promotes modality-invariant gait features. Crucially, our framework decouples generative alignment from the discriminative backbone; the diffusion mechanism serves exclusively as a training objective, ensuring high inference efficiency by eliminating the computational overhead of iterative denoising. Extensive experiments on the SUSTech1K and FreeGait benchmarks demonstrate that DiffCrossGait achieves state-of-the-art performance.

Unlearning in diffusion models aims to remove undesirable data or concepts while preserving the utility of pretrained models -- two fundamentally conflicting objectives. We propose a principled constrained optimization framework that formulates unlearning as minimizing the deviation from a pretrained model, subject to explicit separation constraints from the unlearning distributions. Specifically, we formulate three constrained optimization problems based on reverse and forward KL divergences, and likelihood constraints. The first two generalize existing approaches for concept and data unlearning, while the third offers a novel and natural formulation for unlearning. Despite the nonconvexity of the KL constraints, we establish strong duality for all three problems, enabling us to explicitly characterize their optimal solutions as unlearning targets and develop primal-dual algorithms for each formulation. Experimental results demonstrate that our KL-constrained approach achieves superior retention-unlearning tradeoffs compared to weight-based baselines for concept and data unlearning, and that our likelihood-based approach matches unlearning effectiveness while better preserving retained concepts compared to baselines.

Offline-to-Online Reinforcement Learning (O2O-RL) leverages an offline, pre-trained policy to minimize costly online interactions. Although data-efficient, O2O-RL is susceptible to shifts between offline and online distributions. Existing work aims to mitigate the harm of this shift by finetuning the policy on trajectory data sampled from a diffusion model. Inspired by this line of work, we propose DUAL: an efficient \textbf{D}iffusion \textbf{U}ncertainty-\textbf{A}ware framework for offline-to-online reinforcement \textbf{L}earning. DUAL utilizes the prior knowledge of the diffusion model to distill a fast-sampling diffusion actor policy and transition model in the offline phase. DUAL also employs a Laplace approximation and distance transition-state-shift detection, thereby using uncertainty quantification to improve exploration versus exploitation in the online phase. We formally show that our actor loss with the Laplace approximation provides a proxy for a principled estimate of epistemic uncertainty. Empirically, DUAL improves the online expected return over O2O-RL baselines across multiple settings and environments.

Diffusion-based large language models (dLLMs) support parallel text generation via iterative denoising, yet inference remains latency-heavy because many steps are spent on redundant refinement and repeated remasking of tokens whose final values are already determined. Prior acceleration methods mainly depend on step-local confidence heuristics or fixed schedules, which are sensitive to prompt and task variation and ignore strong positional effects within a sequence. We cast diffusion decoding as a dynamic control problem and show that token-wise denoising trajectories provide the key signal for reliable control. We propose a trace-aware decoding framework with two components. First, Temporal-Spatial Parallel Decoding (TSPD) uses a lightweight temporalspatial controller that consumes per-token trajectory features, including confidence, entropy, and momentum, together with token position, to decide when a token has converged and can be safely fixed. Second, we introduce Confidence Extrapolation (CE), a training-free state-space module that forecasts future logit trends with uncertainty to support proactive decisions, including safe look-ahead and targeted stabilization when trajectories are oscillatory or underconfident. Together, TSPD and CE reduce unnecessary denoising iterations while preserving output quality, and they compose cleanly with system optimizations such as KV caching.

Generative models have a persistent limitation: their tendency to memorize training data can create legal liabilities and erode creative diversity. Understanding which samples are memorized in whole or in part, and under what conditions, therefore remains an important open problem. Here we answer the question "Are atypical or rare samples memorized first?" in the negative. We train diffusion models on strings generated according to the production rules of the Random Hierarchy Model (RHM), and find that samples composed of common substrings are preferentially memorized. This holds true even if the training data consists of entirely unique samples, indicating that deduplication at the data point level does not provide a meaningful privacy guarantee. Correspondingly we predict, then observe, delayed memorization for fat-tailed datasets (i.e., those with more atypical samples). This effect is amplified when fat-tails are introduced into high-level production rules. These together suggest that dataset diversity, particularly at higher levels of abstraction, plays an important role in staving off memorization. Finally, we identify an intermediate regime of partial memorization in which common substrings are learned first and subsequently overproduced during generation. If training is stopped in this regime, models will exhibit the reversion-to-the-mean blandness often derided as "slop".

While automated diagnosis systems have achieved remarkable success in computed tomography (CT)-based lung cancer screening, their development remains limited by the scarcity of diverse, annotated pulmonary nodule datasets. Diffusion-based generative models offer a promising strategy for data synthesis; however, many existing conditional approaches primarily optimize spatial reconstruction losses, which encourage voxel-wise similarity but may inadequately constrain lesion-level intensity distributions. As a result, these methods may produce over-smoothed texture profiles and underrepresent the distinct attenuation characteristics of different nodule subtypes, including solid, part-solid, and ground-glass nodules. To address this challenge, we propose a controllable latent diffusion model that synthesizes pulmonary nodules within full 3D CT volumes while accurately modeling nodule-specific intensity distributions. Specifically, rather than relying solely on spatial losses, we introduce a histogram-based regularization term that constrains voxel intensity distributions during the generative process. The model combines subtype, spatial mask, and Hounsfield unit (HU) histogram conditioning with the differentiable feature-space histogram regularization term to better align lesion-level intensity distributions, improving the visual plausibility and subtype consistency of synthesized nodules. Extensive experiments on lung CT data demonstrate that our framework achieves strong visual realism, validated through both quantitative metrics and a visual Turing test. Furthermore, when used for data augmentation, the generated nodules improve performance in downstream clinical tasks, particularly for underrepresented nodule subtypes, and show a potential benefit for subtype-informed malignancy classification.

With the rise of AI-generated audio, watermarking has become widely used for detecting misuse and protecting intellectual property. However, adversaries may try to remove these watermarks, making it critical to evaluate how well watermarking schemes withstand removal attacks. Existing attacks are often impractical: they either noticeably degrade perceptual quality or require access to the watermarking scheme. We propose DiffErase, a black-box watermark removal attack that assumes no knowledge of the target watermarking scheme while maintaining perceptual quality. DiffErase perturbs watermarked audio to an intermediate diffusion noise level and regenerates it using a pretrained denoising model, effectively suppressing watermark signals. Theoretical analysis and extensive experiments demonstrate that inaudible audio watermarks are highly vulnerable: across multiple audio domains, DiffErase consistently removes watermarks while preserving perceptual quality. These findings highlight the need for future audio watermarking designs to consider diffusion-based threats. Code and demos are available at https://differase.github.io/DiffErase/.

We exhibit an exact correspondence between sampling with score-based diffusion models and adiabatic transport of ground states for a family of Schrödinger operators we call Score Hamiltonians, built from the learned score's quantum potential. We obtain novel density reconstruction bounds and principled annealing schedules via adiabatic theorems for Fokker-Planck equations with time-varying potentials. We find the fundamental limit of sampling is set by the ratio of squared score-matching error to Score Hamiltonian spectral gap - the inverse Poincaré constant of the data density.

Diffusion models achieve state-of-the-art image synthesis, with their generative trajectories fundamentally exhibiting a spectral bias, resolving low-frequency global structures early and high-frequency fine details later. Conventional stochastic differential equation (SDE) solvers fail to account for this dynamic, naively injecting uniform white noise throughout the entire process and misusing the finite energy budget. In this work, we establish a mathematical framework that reconsiders SDE inference as a targeted, frequency-decoupled energy transfer. Leveraging this framework, we introduce Colored Noise Sampling (CNS), a novel, training-free stochastic solver. Rather than injecting uniform white noise, CNS utilizes a dynamic, timestep- and frequency-dependent schedule that more efficiently allocates injected energy toward structurally unresolved frequency bands. By actively exploiting the model's inherent spectral bias, CNS systematically steers the generated distribution toward the true data manifold. Extensive experiments demonstrate that CNS significantly outperforms standard ODE and SDE baselines as a strictly plug-and-play, inference-time sampler substitution across diverse architectures (SiT, JiT, FLUX). Compared to standard sampling on ImageNet-256, CNS achieves substantial unguided FID reductions, improving from 8.26 to 6.27 on SiT-XL/2, 32.39 to 26.69 on JiT-B/16, and 11.88 to 8.31 on JiT-H/16, while yielding consistent relative FID improvements with Classifier-Free Guidance. Project page is available at https://hadardavidson.github.io/CNS/.

This work addresses the problem of recovering complete, simulatable object geometry from reconstructed real-world scenes, enabling physics-based interaction with objects embedded in the scene. While modern multi-view reconstruction methods can produce visually accurate environments, objects are often incomplete due to occlusions and limited observations, making them unsuitable for physics simulation. To address this limitation, we propose SAM3D-Phys, a framework that integrates scene reconstruction with generative 3D priors of SAM3D to recover physically simulatable objects. Our approach first reconstructs the scene from multi-view images to obtain scene geometry and partial observations of objects. We then leverage SAM3D to infer complete object geometry from these partial observations. To ensure that the recovered objects remain consistent with the reconstructed scene, we restore scene-consistent object states through two complementary strategies: a physics-constrained spatial optimization algorithm that iteratively aligns the recovered object to its original location, and a mask-guided appearance distillation module that refines texture fidelity based on the observed images. By recovering complete object geometry and restoring its pose and appearance within the scene, SAM3D-Phys produces clean object representations suitable for physics-based simulation, enabling simultaneous and physically consistent interactive simulation of multiple objects within a reconstructed scene. Project page: https://chnxindong.github.io/sam3d-phys/