Diffusion Models

3D editing has emerged as a critical research area to provide users with flexible control over 3D assets. While current editing approaches predominantly focus on 3D Gaussian Splatting or multi-view images, the direct editing of 3D meshes remains underexplored. Prior attempts, such as VoxHammer, rely on voxel-based representations that suffer from limited resolution and necessitate labor-intensive 3D mask. To address these limitations, we propose VecSet-Edit, the first pipeline that leverages the high-fidelity VecSet Large Reconstruction Model (LRM) as a backbone for mesh editing. Our approach is grounded on a analysis of the spatial properties in VecSet tokens, revealing that token subsets govern distinct geometric regions. Based on this insight, we introduce Mask-guided Token Seeding and Attention-aligned Token Gating strategies to precisely localize target regions using only 2D image conditions. Also, considering the difference between VecSet diffusion process versus voxel we design a Drift-aware Token Pruning to reject geometric outliers during the denoising process. Finally, our Detail-preserving Texture Baking module ensures that we not only preserve the geometric details of original mesh but also the textural information. More details can be found in our project page: https://github.com/BlueDyee/VecSet-Edit/tree/main

Handwritten mathematical expression recognition (HMER) requires reasoning over diverse symbols and structures, yet autoregressive models struggle with exposure bias and syntax inconsistency. We present GryphOne, a discrete diffusion framework which reformulates HMER as iterative symbolic refinement instead of sequential generation. GryphOne progressively refines symbols and relations, removing autoregression and improving consistency. Symbol-aware tokenization and random-masking mutual learning further enhance robustness to handwriting diversity. On the MathWriting benchmark, GryphOne achieves 5.51% CER and 59.9% EM (ExpRate), outperforming all reimplemented models in the matched setting as well as the commercial HMER system. Held-out evaluation on CROHME 2014-2023 further shows strong cross-dataset generalization.

One-Step Diffusion Models have demonstrated promising capability and fast inference in video super-resolution (VSR) for real-world. Nevertheless, the substantial model size and high computational cost of Diffusion Transformers (DiTs) limit downstream applications. While low-bit quantization is a common approach for model compression, the effectiveness of quantized models is challenged by the high dynamic range of input latent and diverse layer behaviors. To deal with these challenges, we introduce LSGQuant, a layer-sensitivity guided quantizing approach for one-step diffusion-based real-world VSR. Our method incorporates a Dynamic Range Adaptive Quantizer (DRAQ) to fit video token activations. Furthermore, we estimate layer sensitivity and implement a Variance-Oriented Layer Training Strategy (VOLTS) by analyzing layer-wise statistics in calibration. We also introduce Quantization-Aware Optimization (QAO) to jointly refine the quantized branch and a retained high-precision branch. Extensive experiments demonstrate that our method has nearly performance to origin model with full-precision and significantly exceeds existing quantization techniques. Code is available at: https://github.com/zhengchen1999/LSGQuant.

Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. For expectations, sampling variability acts as a renormalization of the noise level through a self-consistent relation $σ^2 \mapsto κ(σ^2)$, explaining why limited data overshrink low-variance directions and pull samples toward the dataset mean. For fluctuations, our variance formulas reveal three key factors behind cross-split disagreement: anisotropy across eigenmodes, inhomogeneity across inputs, and overall scaling with dataset size. Extending deterministic-equivalence tools to fractional matrix powers further allows us to analyze entire sampling trajectories. The theory sharply predicts the behavior of linear diffusion models, and we validate its predictions on UNet and DiT architectures in their non-memorization regime, identifying where and how samples deviates across training data split. This provides a principled baseline for reproducibility in diffusion training, linking spectral properties of data to the stability of generative outputs.

As robots are deployed across diverse environments, manipulation tasks require robot hands with different morphologies to satisfy varying task requirements, hardware capabilities, and cost constraints. However, transferring grasping policies learned on one robot hand to another with a different morphology remains a fundamental challenge due to variations in kinematic structures and degrees of freedom across embodiments. To address these limitations, we propose DiffMorphGrasp, the first diffusion-based framework that incorporates hand morphology information into the generative process for cross-embodiment dexterous grasping. The proposed approach maps grasps from diverse robotic hands into a reference hand pose, providing a common space for learning. Grasp generation is then continuously conditioned on structured representations of hand kinematics, encoded as graphs derived from hand configurations, together with object geometry. In addition, we introduce a loss function that computes joint-level errors over the hand kinematic structure to constrain the generated grasps during training. To evaluate DiffMorphGrasp, we construct a new benchmark for assessing grasp generation performance across robot hands with different morphologies. Extensive experiments demonstrate that DiffMorphGrasp achieves strong zero-shot generalization to unseen hand morphologies, enabling scalable cross-embodiment grasp deployment. Project page: https://georgewuzy.github.io/DiffMorphGrasp-website

Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in scientific domains. In this work, we develop a computationally cheap, mathematically justified, and highly flexible distributional modification for combating known pitfalls in equality-constrained generative models. We propose perturbing the data distribution in a constraint-aware way such that the new distribution has support matching the ambient space dimension while still implicitly incorporating underlying manifold geometry. Through theoretical analyses and empirical evidence on several representative tasks, we illustrate that our approach consistently enables data distribution recovery and stable sampling with both diffusion models and normalizing flows.

We revisit diffusion-based generation for structured visual content and identify a fundamental limitation of existing approaches: foreground preservation and background stylization are typically enforced through external interventions, such as hard masking or corrective post-processing, rather than arising from the generative process itself. Here, we define background as the generative content outside designated foreground regions (e.g., text and layout elements), while preserving the structural integrity of the foreground. We propose a dynamical systems perspective on diffusion, in which controllable generation is formulated as trajectory shaping in latent space. Under this view, we introduce Auxiliary Context Diffusion (ACD), a state-space control framework that integrates heterogeneous signals (layout-derived foreground indicators, document summaries, and style representations) directly into the diffusion dynamics. This formulation induces time-scale separation in the generative process, where foreground regions become dynamically stabilized while background regions remain expressive. To address stylistic drift across multi-page documents, we further introduce style directions as persistent latent constraints that guide diffusion trajectories within a shared stylistic subspace. Unlike prior approaches that entangle style with prompt conditioning, our formulation enables reusable and consistent style control across pages. We validate the proposed perspective through controlled experiments on synthetic document benchmarks, demonstrating that trajectory-level control provides a unified and extensible mechanism for structured generation without retraining, hard masking, or corrective post-processing. These results suggest a new direction for controllable diffusion in document-centric and multimodal applications.

We propose two methodologies for modelling aggregated supply and demand curves in the EPEX SPOT Day\char45 Ahead market, emphasizing generative models as a way to recover distributional variability. The first is a low\char45 dimensional parametric representation that yields deterministic point forecasts; the second is a high\char45 dimensional order\char45 level representation that samples from a conditional distribution of plausible curves. Both model the full curve structure, enabling the analysis of price sensitivity, volume sensitivity, and price impact. The parametric representation uses plateau levels, elastic\char45 region boundaries, and polynomial coefficients, forecast with eXtreme Gradient Boosting. The main contribution is the generative representation, which uses price arrivals and volume\char45 increment marks and is implemented with conditional Denoising Diffusion Probabilistic Models. Using French EPEX data from 2021 to 2024, we evaluate both approaches through curve reconstruction and a price\char45 maker storage optimization problem. The parametric implementation provides a deterministic reference, while the diffusion\char45 based implementation produces distributions of plausible curves and achieves higher realized profits and smaller gaps to an oracle benchmark in the storage application.

Diffusion models achieve remarkable generation quality, yet face a fundamental challenge known as memorization, where generated samples can replicate training samples exactly. We develop a theoretical framework to explain this phenomenon by showing that the empirical score function (the score function corresponding to the empirical distribution) is a weighted sum of the score functions of Gaussian distributions, in which the weights are sharp softmax functions. This structure causes individual training samples to dominate the score function, resulting in sampling collapse. In practice, approximating the empirical score function with a neural network can partially alleviate this issue and improve generalization. Our theoretical framework explains why: In training, the neural network learns a smoother approximation of the weighted sum, allowing the sampling process to be influenced by local manifolds rather than single points. Leveraging this insight, we propose two novel methods to further enhance generalization: (1) Noise Unconditioning enables each training sample to adaptively determine its score function weight to increase the effect of more training samples, thereby preventing single-point dominance and mitigating collapse. (2) Temperature Smoothing introduces an explicit parameter to control the smoothness. By increasing the temperature in the softmax weights, we naturally reduce the dominance of any single training sample and mitigate memorization. Experiments across multiple datasets validate our theoretical analysis and demonstrate the effectiveness of the proposed methods in improving generalization while maintaining high generation quality.

Popularized by their strong image generation performance, diffusion and related methods for generative modeling have found widespread success in visual media applications. In particular, diffusion methods have enabled new approaches to data compression, where realistic reconstructions can be generated at extremely low bit-rates. This article provides a unifying review of recent diffusion-based methods for generative lossy compression, with a focus on image compression. These methods generally encode the source into an embedding and use a diffusion model to iteratively refine it during decoding, so that the reconstruction approximately follows the true data distribution. The embedding can take various forms and is typically transmitted via an auxiliary entropy model, and recent methods also explore the use of diffusion models themselves for information transmission via channel simulation. We review representative approaches through the lens of rate-distortion-perception theory, highlighting the role of common randomness and connections to inverse problems, and identify open challenges.

We propose Ambient Dataloops, an iterative framework for refining datasets that makes it easier for diffusion models to learn the underlying data distribution. Modern datasets contain samples of highly varying quality, and training directly on such heterogeneous data often yields suboptimal models. We propose a dataset-model co-evolution process; at each iteration of our method, the dataset becomes progressively higher quality, and the model improves accordingly. To avoid destructive self-consuming loops, at each generation, we treat the synthetically improved samples as noisy, but at a slightly lower noisy level than the previous iteration, and we use Ambient Diffusion techniques for learning under corruption. Empirically, Ambient Dataloops achieve state-of-the-art performance in unconditional and text-conditional image generation and de novo protein design. We further provide a theoretical justification for the proposed framework that captures the benefits of the data looping procedure.

The increasing deployment of deep learning systems requires systematic evaluation of their reliability in real-world scenarios. Traditional gradient-based adversarial attacks introduce small perturbations that rarely correspond to realistic failures and mainly assess robustness rather than functional behavior. Generative test generation methods offer an alternative but are often limited to simple datasets or constrained input domains. Although diffusion models enable high-fidelity image synthesis, their computational cost and limited controllability restrict their applicability to large-scale testing. We present HyNeA, a generative testing method that enables direct and efficient control over diffusion-based generation. HyNeA provides dataset-free controllability through hypernetworks, allowing targeted manipulation of the generative process without relying on architecture-specific conditioning mechanisms or dataset-driven adaptations such as fine-tuning. HyNeA employs a distinct training strategy that supports instance-level tuning to identify failure-inducing test cases without requiring datasets that explicitly contain examples of similar failures. This approach enables the targeted generation of realistic failure cases at substantially lower computational cost than search-based methods. Experimental results show that HyNeA improves controllability and test diversity compared to existing generative test generators and generalizes to domains where failure-labeled training data is unavailable.

Time series generation (TSG) is widely used across domains, yet most existing methods assume regular sampling and fixed output resolutions. These assumptions are often violated in practice, where observations are irregular and sparse, while downstream applications require continuous and high-resolution TS. Although Neural Controlled Differential Equation (NCDE) is promising for modeling irregular TS, it is constrained by a single dynamics function, tightly coupled optimization, and limited ability to adapt learned dynamics to newly generated samples from the generative model. We propose Diff-MN, a continuous TSG framework that enhances NCDE with a Mixture-of-Experts (MoE) dynamics function and a decoupled architectural design for dynamics-focused training. To further enable NCDE to generalize to newly generated samples, Diff-MN employs a diffusion model to parameterize the NCDE temporal dynamics parameters (MoE weights), i.e., jointly learn the distribution of TS data and MoE weights. This design allows sample-specific NCDE parameters to be generated for continuous TS generation. Experiments on ten public and synthetic datasets demonstrate that Diff-MN consistently outperforms strong baselines on both irregular-to-regular and irregular-to-continuous TSG tasks. The code is available at the link https://github.com/microsoft/TimeCraft/tree/main/Diff-MN.

Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available. We propose GenDA, a generative data assimilation framework that reconstructs high-resolution wind fields on unstructured meshes from limited observations. The model employs a multiscale graph-based diffusion architecture trained on computational fluid dynamics (CFD) simulations and interprets classifier-free guidance as a learned posterior reconstruction mechanism: the unconditional branch learns a geometry-aware flow prior, while the sensor-conditioned branch injects observational constraints during sampling. This formulation enables obstacle-aware reconstruction and generalization to held-out mesh geometries, wind directions, and sensor configurations within the studied urban-flow setting, without retraining. We consider both sparse fixed sensors and trajectory-based observations using the same reconstruction procedure. When evaluated against supervised graph neural network (GNN) baselines and classical reduced-order data assimilation methods, GenDA reduces the relative root-mean-square error (RRMSE) by 25-57% and increases the structural similarity index (SSIM) by 23-33% across the tested meshes. Experiments are conducted on Reynolds-averaged Navier-Stokes (RANS) simulations of a real urban neighborhood in Bristol, United Kingdom, at a characteristic Reynolds number of $\mathrm{Re}\approx2\times10^{7}$, featuring complex building geometry and irregular terrain. The proposed framework provides a scalable path toward generative, geometry-aware data assimilation for environmental monitoring in complex domains.

Uniform-noise discrete diffusion and flow models generate sequences non-autoregressively through iterative, context-dependent token replacements. However, these models are typically formulated as time-inhomogeneous continuous- or discrete-time Markov chains (CTMC/DTMC), sampled using independent Bernoulli change decisions per discretization step. This induces Poisson-binomial variance in per-position jump counts that grows with the number of required edits, leading to the common under-editing (residual noise) and over-editing (cascading substitutions) failure modes that degrade sample quality. We identify this sampler-induced variance as an orthogonal source of degradation, distinct from model-side errors and addressable purely at inference time. We propose Systematic Hazard Sampling (SHS), a training-free, drop-in, and hyperparameter-free inference principle for any sampler that admits a stay-vs.-replace decomposition. SHS models per-token edits as events driven by cumulative hazard (CTMC) or jump mass (DTMC) and triggers an edit whenever this quantity exceeds unit-spaced thresholds with a single random phase per position. For any fixed cumulative mass, this preserves the expected jump count while achieving the minimum conditional variance possible among unbiased integer estimators (at most 1/4), without altering per-jump destination sampling. Experiments on four uniform-noise discrete diffusion and flow language models spanning ~110M to ~3B parameters show that SHS consistently improves sample quality across numbers of function evaluations (NFE). Code is available at https://github.com/Jang-seunghwan/Systematic-Hazard-Sampling.

Diffusion models have recently emerged as powerful learners for simulation-based inference (SBI), enabling fast and accurate estimation of latent parameters from simulated and real data. Their score-based formulation offers a flexible way to learn conditional or joint distributions over parameters and observations, thereby providing a versatile solution to various modeling problems. In this tutorial review, we synthesize recent developments on diffusion models for SBI, covering design choices for training, inference, and evaluation. We highlight opportunities created by various concepts such as guidance, score composition, flow matching, consistency models, and joint modeling. Furthermore, we discuss how efficiency and statistical accuracy are affected by noise schedules, parameterizations, and samplers. Finally, we illustrate these concepts with case studies across parameter dimensionalities, simulation budgets, and model types, and outline open questions for future research.

This paper studies the training-testing discrepancy (a.k.a. exposure bias) problem for improving the diffusion models. During training, the input of a prediction network at one training timestep is the corresponding ground-truth noisy data that is an interpolation of the noise and the data, and during testing, the input is the generated noisy data. We present a novel training approach, named MixFlow, for improving the performance. Our approach is motivated by the Slow Flow phenomenon: the ground-truth interpolation that is the nearest to the generated noisy data at a given sampling timestep is observed to correspond to a higher-noise timestep (termed slowed timestep), i.e., the corresponding ground-truth timestep is slower than the sampling timestep. MixFlow leverages the interpolations at the slowed timesteps, named slowed interpolation mixture, for post-training the prediction network for each training timestep. Experiments over class-conditional image generation (including SiT, REPA, and RAE) and text-to-image generation validate the effectiveness of our approach. Our approach MixFlow over the RAE models achieve strong generation results on ImageNet: 1.43 FID (without guidance) and 1.10 (with guidance) at 256 x 256, and 1.55 FID (without guidance) and 1.10 (with guidance) at 512 x 512.

Commercial egocentric devices capture human behavior in everyday settings, yet full-body motion reconstruction must generalize across diverse cameras and mountings. This is challenging because head trajectories under-determine body motion, while hand observations are intermittent and camera-dependent: a hand may disappear simply because it has left the camera's field of view. Existing methods treat such absences as missing data, relying on fixed visibility regimes or post-hoc optimization, and fail to generalize across devices. We present OmniEgoCap, a sequence-level diffusion framework for device-agnostic egocentric full-body motion reconstruction. Our key insight is that egocentric videos contain sequence-level evidence about both the wearer and the camera-induced visibility structure, enabling OmniEgoCap to infer consistent body shape and coherent motion from sparse head and hand cues. To prevent overfitting to a single camera setup, we further introduce geometry-aware visibility augmentation, which synthesizes visibility patterns from realistic variations in camera geometry. We also present OmniEgoDB, the first mocap benchmark that pairs ground-truth motion with recordings from multiple consumer egocentric devices. Experiments on synthetic, real-device, and in-the-wild settings demonstrate superior motion reconstruction, robust cross-device generalization, and coherent in-the-wild results.

Multivariate time series imputation is fundamental in applications such as healthcare, traffic forecasting, and biological modeling, where sensor failures and irregular sampling lead to pervasive missing values. Existing Transformer- and diffusion-based imputers achieve strong performance, but they often rely mainly on time-domain modeling and lack adaptive spectral bias for recovering structured temporal gaps. We propose FADTI, a Fourier- and attention-driven diffusion framework for multivariate time series imputation. FADTI introduces a Fourier Bias Projection (FBP) module that injects learnable frequency-aware bias into intermediate hidden states during denoising. It projects intermediate hidden states onto Fourier bases, avoiding direct spectral estimation from masked or zero-filled inputs. With DFT, STFT, and FSST instantiations, FBP captures global periodicity, localized time--frequency variations, and non-stationary oscillatory patterns. By coupling FBP with self-attention and gated convolution, FADTI integrates frequency-domain guidance, temporal dependency modeling, and probabilistic denoising in a unified framework. Experiments on multiple benchmarks, including a new biological imputation benchmark, show that FADTI improves accuracy, uncertainty estimation, and sampling efficiency, especially under high missing rates and structured missing patterns. Code is available at https://github.com/RazeenLI/FADTI

Automotive radar has shown promising developments in environment perception due to its cost-effectiveness and robustness in adverse weather conditions. However, the limited availability of annotated radar data poses a significant challenge for advancing radar-based perception systems. To address this limitation, we propose a novel framework to generate 4D radar point clouds for training and evaluating object detectors. Unlike image-based diffusion, our method is designed to consider the sparsity and unique characteristics of radar point clouds by applying diffusion to a latent point cloud representation. Within this latent space, generation is controlled via conditioning at either the object or scene level. The proposed 4D-RaDiff converts unlabeled bounding boxes into high-quality radar annotations and transforms existing LiDAR point cloud data into realistic radar scenes. Experiments demonstrate that incorporating synthetic radar data of 4D-RaDiff as data augmentation method during training of object detection models consistently improves performance compared to training on real data only. In addition, pre-training on our synthetic radar data achieves competitive detection performance, providing a promising, scalable approach to reduce dependence on costly manual annotations.

Masked Discrete Diffusion Models (MDMs) have achieved strong performance across a wide range of multimodal tasks, including image understanding, generation, and editing. However, their inference speed remains suboptimal due to the need to repeatedly process redundant masked tokens at every sampling step. In this work, we propose Sparse-LaViDa, a novel modeling framework that dynamically truncates unnecessary masked tokens at each inference step to accelerate MDM sampling. To preserve generation quality, we introduce specialized register tokens that serve as compact representations for the truncated tokens. Furthermore, to ensure consistency between training and inference, we design a specialized attention mask that faithfully matches the truncated sampling procedure during training. Built upon the state-of-the-art unified MDM LaViDa-O, Sparse-LaViDa achieves up to a 2x speedup across diverse tasks including text-to-image generation, image editing, and mathematical reasoning, while maintaining generation quality.

Score-based generative models commonly employ linear forward diffusions with Gaussian reference distributions, limiting their ability to directly incorporate structural information into the noising dynamics. We introduce latent nonlinear denoising score matching (LNDSM), which combines nonlinear, structure-informed latent diffusions with the variational autoencoder (VAE) training framework. In our construction, the forward diffusion is designed to admit a prescribed reference distribution, such as a Gaussian mixture model, that reflects qualitative features of the latent data distribution. We derive a computable approximation to a cross-entropy upper bound in the VAE objective using Euler-Maruyama discretization and the resulting Gaussian conditional transitions. To stabilize training, we remove two zero-mean control variates whose variances become large for small time steps. The resulting objective enables joint training of the encoder, decoder, and latent score network. Numerical experiments on benchmark image datasets demonstrate the effectiveness of LNDSM in learning structured distributions, outperforming conventional latent score-based generative modeling in sample quality and mode balance across several settings, while achieving improved training efficiency. These results highlight the potential of nonlinear, structure-informed latent diffusions for generative modeling.

Real-world deployment of text-to-image diffusion models requires continual concept removal as new privacy, copyright, or safety obligations arise over time. Existing unlearning methods, however, are designed for single-step deletion and collapse after only 3-5 sequential applications. We trace this instability to two compounding factors: (i) coarse mapping targets that cause degradation to accumulate unnecessarily across steps, and (ii) the absence of local protection for semantically neighboring concepts, whose shared internal representations make them the first to suffer collateral damage. Because this damage is strongest in the local semantic neighborhood of the forget concept, global replay alone cannot prevent it. Building on this analysis, we propose Locality-Aware Continual Unlearning (LACU), a framework with two complementary mechanisms. Locality-Aware Target Selection chooses, for each forget prompt, the context-preserving mapping prompt that the diffusion model itself treats as most similar to the original prompt, measured by score-prediction distance (how differently the model denoises the same noisy image under two text conditions), ensuring each update is as small and targeted as possible. Locality-Aware Replay uses the same metric to identify the retain concepts closest to the forget concept in the model's own representation and replays them as a local functional regularizer, directly shielding the most vulnerable neighborhood. Combined with teacher-student distillation and lightweight $\ell_2$ parameter regularization, LACU maintains stable unlearning over 10 sequential steps, preserving significantly higher related retention ($RR_{\text{acc}}$) and general retention ($GR_{\text{acc}}$) than recent baselines.

Modern text-to-image models produce impressive visual results from richly specified prompts, yet their behavior under long prompts remains insufficiently understood. In this paper, we study a practical failure mode in which accumulated semantic constraints progressively suppress output variation, causing diversity to collapse even when many visual factors remain unspecified. We show that this phenomenon appears consistently across recent generation models as prompt length increases, and provide a theoretical motivation that connects long-prompt conditioning with reduced sampling entropy in the prompt embedding space. Based on this observation, we introduce PromptMoG, a training-free approach that samples prompt embeddings from a Mixture-of-Gaussians distribution to restore generative flexibility while maintaining semantic fidelity. To support systematic evaluation, we further present LPD-Bench, a structured benchmark of long and semantically dense prompts for measuring both fidelity and diversity under compositional text conditioning. Extensive experiments on four large-scale diffusion models, including SD3.5-Large, Flux.1-Krea-Dev, CogView4, and Qwen-Image, show that PromptMoG consistently improves diversity for long-prompt image generation. The code is publicly available at https://github.com/basiclab/PromptMoG.

We propose a novel training-free method for inpainting with off-the-shelf text-to-image models. While guidance-based methods in theory allow generic models to be used for inverse problems such as inpainting -- in practice their effectiveness is limited, leading to the necessity of specialized inpainting-specific models. In this work, we argue the missing ingredient for training-free generic model usage is proper optimization of the initial noise sample. We optimize the initial noise to approximately reproduce the unmasked image, in as few as tens of optimization steps, then use it with a conventional training-free inpainting method. Critically, we propose two core ideas that make this possible: (i) we perform linear approximation that avoids the costly and often impractical unrolling required to relate the initial noise sample to model output -- which potentially is why this relationship was previously overlooked; and (ii) perform spectral preconditioning by optimizing the initial noise sample in the spectral domain with Adam, which stabilizes the optimization. We demonstrate our method on various inpainting tasks, outperforming the state of the art. Project website: https://ubc-vision.github.io/sonic/

Camera-controlled video generation has attracted increasing interest for its applications in simulation, gaming, and world modeling. However, current models often deform rigid objects and scene structure as the viewpoint changes. We investigate whether this failure is related to a measurable internal property: the view consistency of diffusion representations. Across a diverse collection of camera-controlled image-to-video diffusion models, we find that models exhibiting more view-consistent representations generate videos with superior 3D consistency. We complement this correlation-based evidence with a within-model controlled intervention, ViCoDR, which directly supervises the view consistency of internal diffusion representations, during training. Across camera-controlled image-to-video, camera-controlled text-to-video, and multi-view generation tasks, ViCoDR consistently improves output 3D consistency. Finally, we evaluate the loss used for these interventions as an auxiliary training objective by retraining a camera-controlled I2V model using either ViCoDR or existing methods for supervising diffusion representations under the same training setup. We show that the ViCoDR loss improves output 3D consistency more reliably than the alternatives and remains effective across design variants, while exhibiting camera-control trade-offs and requiring additional training computation. Together, these results establish view consistency of internal diffusion representations as an important property for analyzing and improving camera-controlled video generation. Project page: https://danier97.github.io/ViCoDR.

Anomaly generation is often framed as few-shot fine-tuning with anomalous samples, which contradicts the scarcity that motivates generation and tends to overfit category priors. We tackle the setting where no real anomaly samples or training are available. We propose Delta-Denoising (DeltaDeno), a training-free zero-shot anomaly generation method that localizes and edits defects by contrasting two diffusion branches driven by a minimal prompt pair under a shared schedule. By accumulating per-step denoising deltas into an image-specific localization map, we obtain a mask to guide the latent inpainting during later diffusion steps and preserve the surrounding context while generating realistic local defects. To improve stability and control, DeltaDeno performs token-level prompt refinement that aligns shared content and strengthens anomaly tokens, and applies a spatial attention bias restricted to anomaly tokens in the predicted region. Experiments on public datasets show that DeltaDeno achieves great generation, realism and consistent gains in downstream detection performance. Code will be made publicly available at https://github.com/CROVO1026/DeltaDeno.

Diffusion models show promise for 3D molecular generation, but face a fundamental trade-off between sampling efficiency and conformational accuracy. While flow-based models are fast, they often produce geometrically inaccurate structures, as they have difficulty capturing the multimodal distributions of molecular conformations. In contrast, denoising diffusion models are more accurate but suffer from slow sampling, a limitation attributed to sub-optimal integration between diffusion dynamics and SE(3)-equivariant architectures. To address this, we propose VEDA, a unified SE(3)-equivariant framework that combines variance-exploding diffusion with annealing to efficiently generate conformationally accurate 3D molecular structures. Specifically, our key technical contributions include: (1) a VE schedule that enables noise injection functionally analogous to simulated annealing, improving 3D accuracy and reducing relaxation energy; (2) a novel preconditioning scheme that reconciles the coordinate-predicting nature of SE(3)-equivariant networks with a residual-based diffusion objective, and (3) a new arcsin-based scheduler that concentrates sampling in critical intervals of the logarithmic signal-to-noise ratio. On the QM9 and GEOM-DRUGS datasets, VEDA matches the sampling efficiency of flow-based models, achieving state-of-the-art valency stability and validity with only 100 sampling steps. More importantly, VEDA's generated structures are remarkably stable, as measured by their relaxation energy during GFN2-xTB optimization. The median energy change is only 1.72 kcal/mol, significantly lower than the 32.3 kcal/mol from its architectural baseline, SemlaFlow. Our framework demonstrates that principled integration of VE diffusion with SE(3)-equivariant architectures can achieve both high chemical accuracy and computational efficiency.

Score-based diffusion models have emerged as a powerful class of generative methods, with successful applications across diverse domains. Despite their empirical success, their mathematical foundations remain only partially understood, particularly regarding the stability and consistency of the stochastic and partial differential equations underlying their dynamics. In this work, we develop a partial differential equation (PDE) framework for score-based diffusion processes associated with the heat flow of a compactly supported data measure. After establishing weak well-posedness on positive-time intervals, we derive a sharp one-sided divergence bound for the score and use it to obtain sharp uniform $L^p$-stability estimates for the generative Fokker--Planck equation. This bound is the Euclidean form of the Li--Yau differential inequality. Through entropy stability methods, we prove that the generated laws converge in the $2$-Wasserstein distance at rate $\sqrt t$ as $t\to0^+$ to a probability measure supported on the data support. This holds for both deterministic and stochastic generation, for positive terminal densities with finite absolute entropy and second moment. In the deterministic case, almost every trajectory converges to a point of the data support; for empirical data, we further obtain a trajectory-wise square-root rate. These results clarify how exact-score dynamics concentrate on the data support without necessarily recovering the data distribution. An explicitly solvable case identifies the limiting weights and their dependence on Gaussian initialization, while a relative-entropy estimate quantifies the effect of score approximation. Together, these findings connect the stability and concentration mechanisms with score learning and early stopping, providing a mathematical perspective on the balance between imitation fidelity and generative diversity.

Generative modeling frameworks have emerged as an effective approach to capture high-dimensional image distributions from large datasets without requiring domain-specific knowledge, a capability essential for disease progression modeling. Recent generative approaches have attempted to capture progression by mapping images to a latent space and guiding representations to generate follow-up images from previous time points. However, these methods impose constraints on distribution learning, resulting in latent spaces with limited controllability for generating follow-up images without paired subject-specific longitudinal guidance. In order to enable controlled movements in the latent representational space and generate progression images from a previous time-point image without subject-specific guidance, we introduce a conditionable Diffusion Auto-encoder framework that forms a compact latent space capturing high-level semantics and providing means to control generation. Our approach leverages this latent space to condition and apply controlled shifts to the representations of previous time-point images by isolating progression and subject identity information for generating follow-up images. The shifts are implicitly guided by correlating with progression attributes and constraining to Alzheimer's disease specific regions, without paired longitudinal guidance. We validate the generations through image quality metrics, volumetric progression analysis, and downstream tasks in Alzheimer's disease datasets from different sources. This demonstrates the effectiveness of our approach for Alzheimer's progression modeling and longitudinal image generation.