Denoising

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.

We argue that training autoencoders to reconstruct inputs from noised versions of their encodings, when combined with perceptually motivated losses, yields encodings that are structured according to a perceptual hierarchy. We demonstrate the emergence of this hierarchy by showing that, after training an audio autoencoder in this manner, perceptually salient information is captured in coarser representation structures than with conventional training. Furthermore, we show that such perceptual hierarchies improve latent diffusion decoding in the context of estimating pitch surprisal in music and predicting EEG-brain responses to music listening. In both cases, our results surpass those of previous methods. Pretrained weights are available on github.com/CPJKU/pa-audioic.

Diffusion-based text-to-video models are increasingly capable, but mask-based editing over hundreds of frames remains challenging: naïve long-video generation suffers from memory blow-up, window seams, and temporal drift, while existing editors often require specialized modules or heavy fine-tuning. We present Overlapping High-Order Co-Denoising, a lightweight framework that turns a single pre-trained text-to-video model into a unified inpainting-outpainting editor. We train only LoRA adapters using mixed interior and border masks together with a dual-region loss that improves synthesis inside the mask while explicitly preserving known content. At inference, we denoise long latent sequences using overlapping windows, apply second-order Heun sampling within each window, and fuse overlaps with Hamming-weighted blending to reduce boundary artifacts and improve temporal coherence. On InpaintBench (30 real-world videos, 81--300 frames), our method outperforms Wan 2.1 variants and VACE in background faithfulness (SSIM/LPIPS), temporal consistency (tLPIPS), and text alignment (CLIP), and scales to long horizons, demonstrated up to 800 frames, with memory bounded by the chosen window size.

License plate image restoration is important not only as a preprocessing step for license plate recognition but also for enhancing evidential value, improving visual clarity, and enabling broader reuse of license plate images. We propose a novel diffusion-based framework with character-level guidance, CharDiff-LP, which effectively restores and recognizes severely degraded license plate images captured under realistic conditions. CharDiff-LP leverages fine-grained character-level priors extracted through external segmentation and Optical Character Recognition (OCR) modules tailored for low-quality license plate images. For precise and focused guidance, CharDiff-LP incorporates a novel Character-guided Attention through Region-wise Masking (CHARM) module, which ensures that each character's guidance is restricted to its own region, thereby avoiding interference with other regions. In experiments, CharDiff-LP significantly outperformed baseline restoration models in both restoration quality and recognition accuracy, achieving a 28.3% relative reduction in character error rate (CER) on the Roboflow-LP dataset compared with the best-performing baseline.

Data unlearning aims to remove the influence of specific training samples from a trained model. In fine-tuning methods, data unlearning relies primarily on loss maximization over forget samples, which often leads to quality degradation or incomplete forgetting. Existing methods perform unlearning uniformly across diffusion stages, ignoring diffusion dynamics from noise to data. Our systematic study of diffusion phases shows that forgetting in diffusion models is uneven across time and frequency, with theoretical justification of distributive distortion and forgetting-utility trade-off. By selectively forgetting time and frequency in diffusion models, we achieve both higher unlearning success rates and improved generation quality across diverse settings, including both conditional and unconditional scenarios. We also introduce an improved SSCD metric that measures dissimilarity using a normalized perturbation distance. Together, we provide practical insights for understanding and improving data unlearning in diffusion models.

Limited-Area Models (LAMs) enable weather forecasting over regional domains at higher resolutions than what is computationally feasible for global models. At such high resolutions, machine learning approaches for weather prediction increasingly rely on ensemble methods to produce probabilistic forecasts. However, existing machine learning LAMs are not scalable due to relying on computationally costly diffusion models or inefficient graph neural networks. We tackle this by introducing a new hybrid CNN/GNN architecture, tailored to the LAM weather forecasting problem. Using this architecture, we construct the DET-LAM deterministic model, producing LAM forecasts both more efficiently and accurately than its graph-based competitor. We then tackle the ensemble forecasting problem, by using this architecture as a backbone for the generative model CRPS-LAM. CRPS-LAM is trained using a Continuous Ranked Probability Score (CRPS) objective, enabling efficient training and sampling in a single forward pass. This yields a speedup of $\approx \times 39$ compared to diffusion-based baselines. We evaluate our approach on regional domains in northern Europe, demonstrating that CRPS-LAM produces skillful and well-calibrated forecasts across a range of atmospheric variables.

Even though more than 30 years have passed since the seminal Rudin--Osher--Fatemi (ROF) paper on total variation (TV) denoising, it remains relevant due to its simplicity, robustness and interpretability. However, it is known to suffer from artifacts such as the staircasing effect. Many variants of the model have been proposed with the aim of countering this. Recently, against the backdrop of immense research output on double-phase problems in the mathematical analysis community, a double-phase type integral functional, comprising of TV and a weighted term of quadratic growth, was suggested as a regularizer for image restoration. Here, we propose an adaptive variant of the ROF denoising model based on that regularizer. Variable growth of the double-phase functional allows for qualitatively different behavior at image contours, which are captured by an initial ROF reconstruction step. The model is designed to reduce staircasing with respect to the classical ROF model, while preserving the edges of the image in a similar fashion. We derive a closed-form resolvent formula and adapt the primal-dual Chambolle--Pock scheme for the numerical solution of the model. We also propose a practical noise-dependent parameter prescription and evaluate its performance on synthetic and natural images over a range of noise levels. Compared to established models with similar interpretability, we observe an improved or similar performance in terms of similarity metrics SSIM, PSNR, and LPIPS, while the staircasing effect is visibly reduced.

Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency Models (CMs) address this limitation by enabling high-quality generation in only one or a few steps, their direct application to inverse problems has remained largely unexplored. This paper introduces a modified consistency sampling framework specifically designed for inverse problems. The proposed approach regulates the sampler's stochasticity through a measurement-consistency mechanism that leverages the degradation operator, thereby enforcing fidelity to the observed data while preserving the computational efficiency of consistency-based generation. Comprehensive experiments on the Fashion-MNIST and LSUN Bedroom datasets demonstrate consistent improvements across both perceptual and pixel-level metrics, including the Fréchet Inception Distance (FID), Kernel Inception Distance (KID), peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM), compared with baseline consistency and diffusion-based sampling methods. The proposed method achieves competitive or superior reconstruction quality with only a small number of sampling steps.

How can we reconstruct 3D hand poses when large portions of the hand are heavily occluded by itself or by objects? Humans often resolve such ambiguities by leveraging contextual knowledge -- such as affordances, where an object's shape and function suggest how the object is typically grasped. Inspired by this observation, we propose a generative prior for hand pose refinement guided by affordance-aware textual descriptions of hand-object interactions (HOI). Our method employs a diffusion-based generative model that learns the distribution of plausible hand poses conditioned on affordance descriptions, which are inferred from a large vision-language model (VLM). This enables the refinement of occluded regions into more accurate and functionally coherent hand poses. Extensive experiments on HOGraspNet, a 3D hand-affordance dataset with severe occlusions, demonstrate that our affordance-guided refinement significantly improves hand pose estimation over both recent regression methods and diffusion-based refinement lacking contextual reasoning.

Solving ill-posed inverse problems requires powerful and flexible priors. We propose leveraging pretrained latent diffusion models for this task through a new training-free approach, termed Diffusion-regularized Wasserstein Gradient Flow (DWGF). Specifically, we formulate the posterior sampling problem as a Wasserstein gradient flow in the latent space of an expected negative log posterior objective, regularized by a Kullback-Leibler divergence to the diffusion prior. We demonstrate the performance of our method on standard benchmarks using StableDiffusion (Rombach et al., 2022) as the prior.

Few-shot 3D point cloud semantic segmentation aims to segment novel categories using a minimal number of annotated support samples. However, prototypes derived from the limited non-structural point cloud support set are often misaligned and have a small capacity, hindering effective gen eralization to novel categories. This stems from two core issues: i) the prototype possess limited representational capacity fails to cover the full intra-class diversity of a novel category, and ii) the prototypes suffer from misalignment with the query space due to the inter-set inconsistency between support and query sets. To address these issues, our work focuses on leveraging the few support samples to construct a well-aligned big-capacity prototype. Motivated by the powerful generative capabilities of diffusion models, we re-purpose its pre-trained conditional encoder to provide rich feature components for prototype ex pansion. Subsequently, a push-pull force aligns this expanded prototype towards the query feature space. Under this setup, we introduce the Prototype Expansion Network (PENet), a framework that constructs aligned big-capacity prototypes from two complementary feature sources. Specifically, PENet employs a dual-stream learner architecture: it retains a conventional fully supervised Intrinsic Learner (IL) to distill representative features, while introducing a novel Diffusion Learner (DL) to provide rich generalizable features. The resulting dual prototypes are then processed by a Prototype Assimilation Module (PAM), which adopts a push-pull attention block to align the prototypes with the query space. Furthermore, a Prototype Calibration Mechanism (PCM) regularizes the final big-capacity prototype to prevent semantic drift. Extensive experiments on the S3DIS and ScanNet datasets demonstrate that PENet outperforms state-of-the-art methods across various few-shot settings.

Recent advances in self-supervised learning for EEG representation have largely relied on masked reconstruction, where models are trained to recover randomly masked signal segments. While effective at modeling local dependencies, the training objective of masked reconstruction does not compel the model to capture global generative constraints essential for characterizing neural activity. To address this limitation, we propose EEGDM, a novel self-supervised framework that leverages latent diffusion models to generate EEG signals as an objective. Unlike masked reconstruction, diffusion-based generation progressively denoises signals from noise to realism, compelling the model to capture holistic temporal patterns and cross-channel relationships. Specifically, EEGDM incorporates an EEG encoder that distills raw signals and their channel augmentations into a compact representation, which serves as conditional information to guide the diffusion denoising process, thereby enabling the encoder and diffusion model to be jointly optimized through the generative objective. This design endows EEGDM with a compact latent space, which not only offers ample control over the generative process but also can be leveraged for downstream tasks. Experimental results show that EEGDM (1) reconstructs high-quality EEG signals, (2) learns robust representations, and (3) achieves competitive performance across diverse downstream tasks, thus exploring a new direction for self-supervised EEG representation learning.

Low-dose computed tomography (CT) denoising is crucial for reduced radiation exposure while ensuring diagnostically acceptable image quality. Despite significant advancements driven by deep learning (DL) in recent years, existing DL-based methods, typically trained on a specific dose level and anatomical region, struggle to handle diverse noise characteristics and anatomical heterogeneity during varied scanning conditions, limiting their generalizability and robustness in clinical scenarios. In this paper, we propose FoundDiff, a foundational diffusion model for unified and generalizable LDCT denoising across various dose levels and anatomical regions. FoundDiff employs a two-stage strategy: (i) dose-anatomy perception and (ii) adaptive denoising. First, we develop a dose- and anatomy-aware contrastive language-image pre-training model (DA-CLIP) to achieve robust dose and anatomy perception by leveraging specialized contrastive learning strategies to learn continuous representations that quantify ordinal dose variations and identify salient anatomical regions. Second, we design a dose- and anatomy-aware diffusion model (DA-Diff) to perform adaptive and generalizable denoising by synergistically integrating the learned dose and anatomy embeddings from DA-CLIP into diffusion process via a novel dose and anatomy conditional block (DACB) based on Mamba. Extensive experiments on a large simulated multi-dose CT dataset spanning three anatomical regions, together with cross-dataset evaluations on Mayo-2016, CQ500, and piglet datasets, demonstrate superior denoising performance and strong generalization to unseen dose levels and anatomical regions. The codes and models are available at https: //github.com/hao1635/FoundDiff.

While video generation models excel at producing high-quality monocular videos, generating 3D stereoscopic and spatial videos for immersive applications remains an underexplored challenge. We present a pose-free and training-free method that leverages an off-the-shelf monocular video generation model to produce immersive 3D videos. Our approach first warps the generated monocular video into pre-defined camera viewpoints using estimated depth information, then applies a novel \textit{frame matrix} inpainting framework. This framework utilizes the original video generation model to synthesize missing content across different viewpoints and timestamps, ensuring spatial and temporal consistency without requiring additional model fine-tuning. Moreover, we develop a \dualupdate~scheme that further improves the quality of video inpainting by alleviating the negative effects propagated from disoccluded areas in the latent space. The resulting multi-view videos are then adapted into stereoscopic pairs or optimized into 4D Gaussians for spatial video synthesis. We validate the efficacy of our proposed method by conducting experiments on videos from various generative models, such as Sora, Lumiere, WALT, and Zeroscope. The experiments demonstrate that our method has a significant improvement over previous methods. Project page at: https://daipengwa.github.io/S-2VG_ProjectPage/

3D affordance grounding aims to understand how diverse objects can be manipulated, making it a cornerstone of embodied interaction. However, prior works struggle to generalize to out-of-distribution, open-world scenarios, leaving a critical gap between limited dataset performance and real-world application needs. Inspired by the saying: \textit{\textbf{``What I can not create, I do not understand''}}, we find generative models can generate semantically valid HOI images, which indicates inherent encoding of affordance concepts. Building on this insight, we propose DAG, the first innovative diffusion-based 3D affordance grounding framework that extracts general affordance knowledge from text-to-image diffusion models for 3D affordance prediction. Specifically, we extract the affordance priors from a diffusion model to encode HOI priors, and design an affordance block with a multi-source affordance decoder for dense 3D affordance prediction. Extensive experiments show that DAG consistently outperforms state-of-the-art methods and exhibits strong open-world generalization, even in the challenging one-shot setting. The code of our method is released on \textcolor{blue}{\textit{https://github.com/hq-King/DAG}}.

Training data for class-conditional image synthesis often exhibit a long-tailed distribution with limited amount of images for tail classes. Such an imbalance causes mode collapse and reduces the diversity of synthesized images for tail classes. For class-conditional diffusion models trained with imbalanced data, we aim to improve the diversity and fidelity of tail class images without compromising the quality of head class images. We propose contrastive conditional-unconditional alignment (CCUA), which comprises two synergistic loss functions. Our first loss is an Alignment Loss (AL) that aligns class-conditional generation with unconditional generation at large timesteps. Alignment loss makes the denoising process insensitive to class conditions for the initial steps, which enriches tail classes through knowledge sharing from head classes. Secondly, we diversify unconditional generation via an Unsupervised Contrastive Loss (UCL) to increase the distance/dissimilarity among synthetic images. We combine the two losses to implicitly diversify conditional generation. Our framework is easy to implement as demonstrated on both U-Net based architecture and Diffusion Transformer. Our method outperforms vanilla denoising diffusion probabilistic models, score-based diffusion model, and alternative contrastive methods for class-imbalanced image generation across various datasets, in particular ImageNet-LT with 256$\times$256 resolution.

Typically, numerical simulations of Earth systems are coarse, and Earth observations are sparse and gappy. We apply four generative diffusion modeling approaches to super-resolution and inference of forced two-dimensional quasi-geostrophic turbulence on the beta-plane from coarse, sparse, and gappy observations. Two guided approaches minimally adapt a pre-trained unconditional model: SDEdit modifies the initial condition, and Diffusion Posterior Sampling (DPS) modifies the reverse diffusion process score. Two conditional approaches, a vanilla variant and classifier-free guidance, require training with paired high-resolution and observation data. We consider multiple test cases spanning: two regimes, eddy and anisotropic-jet turbulence; two Reynolds numbers, 10^3 and 10^4; and two observation types, 4x coarse-resolution fields and coarse, sparse and gappy observations. Our comprehensive skill metrics include norms of the reconstructed vorticity fields, turbulence statistical quantities, and quantifications of the super-resolved probabilistic ensembles and their errors. We also study the sensitivity to tuning parameters such as guidance strength. Results show that the generated super-resolution fields of SDEdit are unphysical, while those of DPS are reasonable but with smoothed fine-scale features; however, neither of these lower-cost models propagates observational information effectively to unobserved regions. The two conditional models require re-training, but reconstruct missing fine-scale features, are cycle-consistent with observations, and predict correct turbulence statistics, including the tails. Further, their mean errors are highly correlated with and predictable from their ensemble standard deviations. Results highlight the tradeoffs between ease of implementation, fidelity (sharpness), and cycle-consistency of the diffusion models, and offer practical guidance for deployment.

Urban sensor networks need forecasts that are accurate, carry useful uncertainty, and refresh fast enough to act on as new readings arrive. These goals conflict: deterministic models give no distribution, while diffusion forecasters model uncertainty but denoise from pure noise over many steps. We present Double-Diffusion, which integrates a closed-form graph-heat prior into a denoising diffusion model. The prior is a parameter-free low-pass forecast over the sensor graph, and it serves two roles: it is the residual target the model generates, and it conditions the denoiser. The reverse process therefore starts near the prior and denoises a short warm-started chain instead of synthesizing from pure noise; the name denotes this composition, a graph diffusion feeding a denoising diffusion. A compact denoiser, DD-Net, is trained as a Denoising Diffusion Probabilistic Model (DDPM) in the Resfusion warm-start formulation, so generation refines the prior over a short truncated chain rather than synthesizing from pure noise; a graph-spectral read-out of the prior residual sets its switchable spatial filter per domain from training data alone. On four real-world air quality and traffic networks, Double-Diffusion attains the best CRPS of all probabilistic methods on every dataset and stays competitive in point accuracy with the strongest baselines, at a fraction of the sampling cost of from-noise diffusion. The code is available at: https://github.com/teddyicare/Double-Diffusion

Diffusion models generate conditional samples by progressively denoising Gaussian noise, yet the denoising trajectory can stall at visually plausible but low-quality outcomes with conditional misalignment or structural artifacts. We interpret this behavior as local optima in a surrogate quality landscape: Once early denoising commits to a suboptimal global structure, later steps mainly sharpen details and seldom correct the underlying mistake. While existing inference-time approaches explore alternative diffusion states via re-noising with fixed strength or direction, they exhibit limited capacity to escape steep quality plateaus. We propose Controlled Random Zigzag Sampling (Ctrl-Z Sampling),a scalable sampling strategy that detects plateaus in quality landscape via a surrogate score, and allocates exploration only when a plateau is detected. Upon detection, Ctrl-Z Sampling rolls back to noisier states, samples a set of alternative continuations, and updates the trajectory when a candidate improves the score, otherwise escalating the exploration depth to escape the current plateau. The proposed method is model-agnostic and broadly compatible with existing diffusion frameworks. Experiments show that Ctrl-Z Sampling consistently improves generation quality over other inference-time scaling samplers across different NFE budgets, offering a scalable compute-quality trade-off. Code available at: https://github.com/ShunqiM/Ctrl-Z-Sampling.

Multi-person pose estimation (MPPE), which involves detecting body joint positions (keypoints) for every person in an image, is a fundamental task in computer vision. Despite recent advances, no transformer-based model currently achieves real-time performance. This work addresses the latency challenge by introducing DETRPose, the first family of real-time, end-to-end transformer models for multi-person 2D pose estimation. DETRPose significantly enhances the GroupPose decoder, enabling real-time inference. For training, a novel denoising keypoint technique is proposed to accelerate convergence. The varifocal loss is also extended for keypoints, termed Keypoint Similarity VariFocal loss, to improve query quality. Extensive evaluation demonstrates that DETRPose models achieve accuracy comparable to or exceeding that of leading alternatives while requiring five to ten times fewer training epochs. DETRPose-S matches the accuracy of YOLOv8-Pose-X and YOLO11-Pose-X on the COCO dataset (67.0 vs 67.3 and 67.2 in AP) with 81% fewer parameters (11.5M vs 69.4M and 58.8M) and 52% faster inference speed (2.39ms vs 5.23ms and 4.93ms). On the CrowdPose dataset, DETRPose-X has $13.1\times$ fewer FLOPs (232.3G vs 3048.1G) and only $2$ fewer precision (75.1 vs 76.6 in AP) than ED-Pose-SwinL-5S. On the OCHuman dataset, DETRPose-S surpasses all previous models, showing the robustness of DETRPose on out-of-distribution datasets. Code is available at https://github.com/SebastianJanampa/DETRPose

Sampling in score-based diffusion models can be performed by solving either a reverse-time stochastic differential equation (SDE) parameterized by an arbitrary stochasticity function or a probability flow ODE, corresponding to setting this stochasticity function to zero. In this work, we investigate the effect of this stochasticity on the generation process through the evolution of Kullback-Leibler (KL) divergences, obtaining general KL divergence bounds and a novel analysis of the impact of the time-profile of the score error on model performance. For exact score functions, stochasticity has a contractive effect, decreasing KL divergence along the sampling trajectory. For approximate scores, however, a trade-off arises between correcting accumulated errors and amplifying current score errors, meaning stochasticity can either improve or degrade generation performance. Theoretical considerations indicate that the gain from stochasticity depends on the time-localization of the trained model error. We test this in experiments on both toy and benchmark data sets, also comparing the KL divergence evolution with the obtained bounds. We also present a fully analytical example, where all the relevant quantities can be computed, and the optimal stochasticity function can be characterized via an optimal control analysis.

Latent Diffusion Models have shown remarkable results in text-guided image synthesis in recent years. In the domain of natural (RGB) images, recent works have shown that such models can be adapted to various vision-language downstream tasks with little to no supervision involved. On the contrary, text-to-image Latent Diffusion Models remain relatively underexplored in the field of medical imaging, primarily due to limited data availability (e.g., due to privacy concerns). In this work, focusing on the chest X-ray modality, we first demonstrate that a standard text-conditioned Latent Diffusion Model has not learned to align clinically relevant information in free-text radiology reports with the corresponding areas of the given scan. Then, to alleviate this issue, we propose a fine-tuning framework to improve multi-modal alignment in a pre-trained model such that it can be efficiently repurposed for downstream tasks such as phrase grounding. Our method sets a new state-of-the-art on a standard benchmark dataset (MS-CXR), while also exhibiting robust performance on out-of-distribution data (VinDr-CXR). We further validate our approach through a pilot qualitative study and an experiment on grounded disease classification. Our code will be made publicly available at https://github.com/vios-s.

Synthetic data generation is increasingly used in machine learning for training and data augmentation. Yet, current strategies often rely on external foundation models or datasets, whose usage is restricted in many scenarios due to policy or legal constraints. We propose ScoreMix, a self-contained synthetic generation method to produce hard synthetic samples for recognition tasks by leveraging the score compositionality of diffusion models. The approach mixes class-conditioned scores along reverse diffusion trajectories, yielding domain-specific data augmentation without external resources. We systematically study class-selection strategies and find that mixing classes distant in the discriminator's embedding space yields larger gains, providing up to 3% additional average improvement, compared to selection based on proximity. Interestingly, we observe that condition and embedding spaces are largely uncorrelated under standard alignment metrics, and the generator's condition space has a negligible effect on downstream performance. Across 8 public face recognition benchmarks, ScoreMix improves accuracy by up to 7 percentage points, without hyperparameter search, highlighting both robustness and practicality. Our method provides a simple yet effective way to maximize discriminator performance using only the available dataset, without reliance on third-party resources. Paper website: https://parsa-ra.github.io/scoremix/.

Generating semantically controllable 3D CT volumes from radiology reports requires more than a rich text encoder, it requires vision-language alignment grounded in volumetric space. Existing Text-to-CT approaches condition generation on encoders pretrained with language only or 2D vision-language objectives, providing conditioning signals that are linguistically expressive but volumetrically blind. We argue this is a structural limitation: the quality of 3D vision-language alignment, not the richness of the text encoder, is the primary bottleneck for semantic controllability in volumetric diffusion models. To address this, we propose a generation-oriented 3D-CLIP encoder trained with structured hard negatives that operate exclusively at the text level. This design increases contrastive difficulty without any additional 3D memory cost, overcoming the small-batch constraints inherent to volumetric encoders. The resulting encoder conditions a fully end-to-end latent diffusion model that operates directly in 3D latent space, eliminating the spatial artifacts and cross-slice inconsistencies introduced by super-resolution pipelines. Through systematic ablations, we establish a clear empirical link between grounding quality and downstream generative controllability. Evaluated on CT-RATE across 18 pathological conditions, our method achieves state-of-the-art performance on both image fidelity and factual correctness, while requiring less inference time and GPU memory than all competing methods. Code is at https://github.com/danielemolino/Text2CT.

Rapid urbanization demands efficient monitoring of turbulent wind and pollutant dispersion, yet existing reconstruction and sensor placement strategies fail under realistic sparsity constraints. Here, we introduce Diff--SPORT, a diffusion-based framework that combines a generative diffusion prior with maximum a posteriori inference and Shapley-value attribution for high-fidelity flow reconstruction and optimal sensor placement. By training a diffusion prior model once over a domain, Diff--SPORT enables non-linear optimal sensor placement and near-real-time flow reconstruction from sparse measurements orders of magnitude faster than RANS or LES simulations, consistently outperforming state-of-the-art methods. The framework also extends, without algorithmic modification, to experimental passive scalar concentration dataset, a direct proxy for pollutant dispersion, measured in a 1:2400 scale water-flume model of the Beijing Haidian neighbourhood under realistic urban flow conditions. Shapley-guided sensor placement achieves up to 57% lower reconstruction error than randomly placed sensors at extreme sparsity, identifying compact and physically interpretable configurations. These results establish Diff--SPORT as a modular foundation offering a zero-shot alternative to retraining-intensive downstream strategies, supporting scalable urban flow monitoring for air quality management and resilient city design.

Image demoiréing remains a challenging task due to the complex interplay between texture corruption and color distortions caused by moiré patterns. Existing methods, especially those relying on direct image-to-image restoration, often fail to disentangle these intertwined artifacts effectively. While frequency-aware approaches offer a promising direction, their potential is hindered by the discrete transform (e.g., Haar wavelet or block-based DCT), which may suffer from spatial discontinuity, channel redundancy, and further cause error accumulation during their fixed inverse processes. In this paper, we present Freqformer, a Transformer-based framework specifically designed for image demoiréing through targeted frequency separation. Our method performs an effective frequency decomposition that splits moiré patterns into high-frequency spatially-localized textures and low-frequency scale-robust color distortions, which are then handled by a dual-branch architecture and an asymmetric training scheme tailored to their distinct characteristics. We further propose a learnable Frequency Composition Transform (FCT) module to adaptively fuse the frequency-specific outputs, enabling consistent and high-fidelity reconstruction. To better aggregate the spatial dependencies and the inter-channel complementary information, we introduce a Spatial-Aware Channel Attention (SA-CA) module that refines moiré-sensitive regions without incurring high computational cost. Extensive experiments on various demoiréing benchmarks demonstrate that Freqformer achieves state-of-the-art performance with a compact model size. The code will be made publicly available at https://github.com/xyLiu339/Freqformer.

The substantial training cost of diffusion models hinders their deployment. Immiscible Diffusion recently showed that reducing diffusion trajectory mixing in the noise space via linear assignment accelerates training by simplifying denoising. To extend immiscible diffusion beyond the inefficient linear assignment under high batch sizes and high dimensions, we refine this concept to a broader miscibility reduction at any layer and by any implementation. Specifically, we empirically demonstrate the bijective nature of the denoising process with respect to immiscible diffusion, ensuring its preservation of generative diversity. Moreover, we provide thorough analysis and show step-by-step how immiscibility eases denoising and improves efficiency. Extending beyond linear assignment, we propose a family of implementations including K-nearest neighbor (KNN) noise selection and image scaling to reduce miscibility, achieving up to >4x faster training across diverse models and tasks including unconditional/conditional generation, image editing, and robotics planning. Furthermore, our analysis of immiscibility offers a novel perspective on how optimal transport (OT) enhances diffusion training. By identifying trajectory miscibility as a fundamental bottleneck, we believe this work establishes a potentially new direction for future research into high-efficiency diffusion training. The code is available at https://github.com/yhli123/Immiscible-Diffusion.

Modern Vision-Language Models (VLMs) can solve a wide range of tasks requiring visual reasoning. In real-world scenarios, desirable properties for VLMs include fast inference and controllable generation (e.g., constraining outputs to adhere to a desired format). However, existing autoregressive (AR) VLMs like LLaVA struggle in these aspects. Discrete diffusion models (DMs) offer a promising alternative, enabling parallel decoding for faster inference and bidirectional context for controllable generation through text-infilling. While effective in language-only settings, DMs' potential for multimodal tasks is underexplored. We introduce LaViDa, a family of VLMs built on DMs. We build LaViDa by equipping DMs with a vision encoder and jointly fine-tune the combined parts for multimodal instruction following. To address challenges encountered, LaViDa incorporates novel techniques such as complementary masking for effective training, prefix KV cache for efficient inference, and timestep shifting for high-quality sampling. Experiments show that LaViDa achieves competitive or superior performance to AR VLMs on multi-modal benchmarks such as MMMU, while offering unique advantages of DMs, including flexible speed-quality tradeoff, controllability, and bidirectional reasoning. On COCO captioning, LaViDa surpasses Open-LLaVa-Next-8B by +4.1 CIDEr with 1.92x speedup. On bidirectional tasks, it achieves +59% improvement on Constrained Poem Completion. These results demonstrate LaViDa as a strong alternative to AR VLMs. Code and models will be released in the camera-ready version.

Diffusion models now serve as a common foundation for multimedia generation, and useful intermediate representations emerge during their generative training. Standard architectures, however, propagate these representations through the main feature stream, without explicitly reintroducing their encoded semantics to later denoising layers. Meanwhile, such backbones already provide a conditioning pathway for global modulation by predefined inputs. This work examines whether this native pathway can also route internally inferred semantics as evolving, sample-dependent cues. We propose Conditioning Residuals, a lightweight feedback mechanism that converts aggregated features into residuals added to condition embeddings. By feeding back compact feature summaries, it provides adaptive generative guidance and encourages a tighter semantic bottleneck, without external encoders, auxiliary objectives, or sampling-time changes. It supports feedback at one or multiple depths in UNet and DiT backbones, with negligible overhead. Across diffusion formulations, backbone configurations, and datasets, experiments show consistent gains in generative performance, along with stronger representations in downstream linear probing and segmentation. Mechanistic analyses reveal improved generative training dynamics and reshaped feature structure, suggesting a grounded, generalizable way to enhance diffusion backbones from within.

Face Anti-Spoofing (FAS) is essential for the security of facial recognition systems in diverse scenarios such as payment processing and surveillance. Current multimodal FAS methods often struggle with effective generalization, mainly due to modality-specific biases and domain shifts. To address these challenges, we introduce the \textbf{M}ulti\textbf{m}odal \textbf{D}enoising and \textbf{A}lignment (\textbf{MMDA}) framework. By leveraging the zero-shot generalization capability of CLIP, the MMDA framework effectively suppresses noise in multimodal data through denoising and alignment mechanisms, thereby significantly enhancing the generalization performance of cross-modal alignment. The \textbf{M}odality-\textbf{D}omain Joint \textbf{D}ifferential \textbf{A}ttention (\textbf{MD2A}) module in MMDA concurrently mitigates the impacts of domain and modality noise by refining the attention mechanism based on extracted common noise features. Furthermore, the \textbf{R}epresentation \textbf{S}pace \textbf{S}oft (\textbf{RS2}) Alignment strategy utilizes the pre-trained CLIP model to align multi-domain multimodal data into a generalized representation space in a flexible manner, preserving intricate representations and enhancing the model's adaptability to various unseen conditions. We also design a \textbf{U}-shaped \textbf{D}ual \textbf{S}pace \textbf{A}daptation (\textbf{U-DSA}) module to enhance the adaptability of representations while maintaining generalization performance. These improvements not only enhance the framework's generalization capabilities but also boost its ability to represent complex representations. Our experimental results on four benchmark datasets under different evaluation protocols demonstrate that the MMDA framework outperforms existing state-of-the-art methods in terms of cross-domain generalization and multimodal detection accuracy. The code will be released soon.

We present StableMotion, a novel framework that leverages geometric and content priors from pretrained large-scale image diffusion models for motion estimation in single-image rectification tasks such as Stitched Image Rectangling (SIR) and Rolling Shutter Correction (RSC). Specifically, StableMotion takes a text-to-image Stable Diffusion (SD) model as its backbone and repurposes it as an image-to-motion estimator. To mitigate inconsistent outputs produced by diffusion models, we propose Adaptive Ensemble Strategy (AES), which consolidates multiple outputs into a cohesive, high-fidelity result. Additionally, we present Sampling Steps Disaster (SSD), a counterintuitive phenomenon in which increasing the number of sampling steps can lead to poorer outcomes, motivating our one-step inference design. StableMotion is evaluated on two image rectification tasks and delivers state-of-the-art performance on both, while also showing promising transferability through qualitative examples and no-reference evaluations on unseen SIR-OOD and real-captured RSC benchmarks. Supported by SSD, StableMotion achieves efficient one-step inference, offering over 100$\times$ speedup compared to previous diffusion model-based methods even when combined with the optional AES post-processing. Code and weights are available at https://github.com/ivowang/StableMotion.

Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, a task that in principle suffers from the curse of dimensionality. It is therefore important to understand how low-dimensional structure in the target distribution can be exploited in these models. Here we consider locality structure, which describes certain sparse conditional dependencies among the target random variables. Given some locality structure, the score function is effectively low-dimensional, so that it can be estimated by a localized neural network with significantly reduced sample complexity. This observation motivates the localized diffusion model, where a localized score matching loss is used to train the score function within a localized hypothesis space. We prove that such localization enables diffusion models to circumvent the curse of dimensionality with dimension-independent error bounds, at the price of additional localization error. Under realistic sample size scaling, we then show both theoretically and numerically that a moderate localization radius can balance the statistical and localization errors, yielding better overall performance. Locality structure also facilitates parallel training, making localized diffusion models potentially more efficient for large-scale applications.

We propose Riemannian Denoising Diffusion Probabilistic Models (RDDPMs) for learning distributions on submanifolds of Euclidean space that are level sets of functions, including most of the manifolds relevant to applications. Existing methods for generative modeling on manifolds rely on substantial geometric information such as geodesic curves or eigenfunctions of the Laplace-Beltrami operator and, as a result, they are limited to manifolds where such information is available. In contrast, our method, built on a projection scheme, can be applied to more general manifolds, as it only requires being able to evaluate the value and the first order derivatives of the function that defines the submanifold. We provide a theoretical analysis of our method in the continuous-time limit, which elucidates the connection between our RDDPMs and score-based generative models on manifolds. The capability of our method is demonstrated on datasets from previous studies and on new datasets sampled from two high-dimensional manifolds, i.e. $\mathrm{SO}(10)$ and the configuration space of molecular system alanine dipeptide with fixed dihedral angle.

We present a bifidelity method for uncertainty quantification of parameter estimates in complex systems, leveraging generative models trained to sample the target conditional distribution. In the Bayesian inference setting, traditional parameter estimation methods rely on repeated simulations of potentially expensive forward models to determine the posterior distribution of the parameter values, which may result in computationally intractable workflows. Furthermore, methods such as Markov Chain Monte Carlo (MCMC) necessitate rerunning the entire algorithm for each new data observation, further increasing the computational burden. Hence, we propose a novel method for efficiently obtaining posterior distributions of parameter estimates for high-fidelity models given data observations of interest. The method first constructs a low-fidelity, conditional generative model capable of amortized Bayesian inference and hence rapid posterior density approximation over a wide-range of data observations. When higher accuracy is needed for a specific data observation, the method employs adaptive refinement of the density approximation. It uses outputs from the low-fidelity generative model to refine the parameter sampling space, ensuring efficient use of the computationally expensive high-fidelity solver. Subsequently, a high-fidelity, unconditional generative model is trained to achieve greater accuracy in the target posterior distribution. Both low- and high- fidelity generative models enable efficient sampling from the target posterior and do not require repeated simulation of the high-fidelity forward model. We demonstrate the effectiveness of the proposed method on several numerical examples, including cases with multi-modal densities, as well as an application in plasma physics for a runaway electron simulation model.

Supervised deep learning achieves strong performance in biomedical image segmentation but relies on costly pixel-wise annotations, motivating semi-supervised approaches that exploit unlabeled data. We introduce a diffusion-based teacher--student framework in which segmentation predictions are used to condition image denoising, encouraging the production of more informative pseudo-labels. The teacher is first pretrained through an unsupervised reconstruction task using diffusion-style corruption, timestep conditioning, and denoising. Starting from a corrupted empty mask, the model predicts an intermediate segmentation that conditions image denoising, encouraging the predicted mask to capture structural information useful for recovering the original image. The resulting teacher is then co-trained with a student using supervised segmentation on labeled samples and cross pseudo-supervision on unlabeled data. We further introduce a multi-round extension during co-training, in which the teacher generates multiple stochastic image reconstructions and corresponding segmentation predictions, providing additional reconstruction and alignment signals to improve its pseudo-labels. We evaluate the proposed framework on three public 2D biomedical segmentation datasets and a 3D left atrial segmentation benchmark. Across several labeling regimes, our method achieves competitive or superior performance compared with state-of-the-art semi-supervised approaches, with the largest gains observed under severe label scarcity.

Image generation algorithms are increasingly integral to diverse aspects of human society, driven by their practical applications. However, insufficient oversight in artificial Intelligence generated content (AIGC) can facilitate the spread of malicious content and increase the risk of copyright infringement. Among the diverse range of image generation models, the Latent Diffusion Model (LDM) is currently the most widely used, dominating the majority of the Text-to-Image model market. Currently, most attribution methods for LDMs rely on directly embedding watermarks into the generated images or their intermediate noise, a practice that compromises both the quality and the robustness of the generated content. To address these limitations, we introduce TraceMark-LDM, an novel algorithm that integrates watermarking to attribute generated images while guaranteeing non-destructive performance. Unlike current methods, TraceMark-LDM leverages watermarks as guidance to rearrange random variables sampled from a Gaussian distribution. To mitigate potential deviations caused by inversion errors, the small absolute elements are grouped and rearranged. Additionally, we fine-tune the LDM encoder to enhance the robustness of the watermark. Experimental results show that images synthesized using TraceMark-LDM exhibit superior quality and attribution accuracy compared to state-of-the-art (SOTA) techniques. Notably, TraceMark-LDM demonstrates exceptional robustness against various common attack methods, consistently outperforming SOTA methods.

This work presents an optimization method for generating kinodynamically feasible and collision-free multi-robot trajectories that exploits an incremental denoising scheme in diffusion models. Our key insight is that high-quality trajectories can be discovered merely by denoising noisy trajectories sampled from a distribution. This approach has no learning component, relying instead on only two ingredients: a dynamical model of the robots to obtain feasible trajectories via rollout, and a fitness function to guide denoising with Monte Carlo gradient approximation. The proposed framework iteratively optimizes a deformation for the previous trajectory with the current denoising process, allows anytime refinement as time permits, supports different dynamics, and benefits from GPU acceleration. Our evaluations for differential-drive and holonomic teams with up to 16 robots in 2D and 3D worlds show its ability to discover high-quality solutions faster than other black-box optimization methods such as MPPI. In a 2D holonomic case with 16 robots, it is almost twice as fast. As evidence for feasibility, we demonstrate zero-shot deployment of the planned trajectories on eight multirotors. Code and video: https://github.com/proroklab/d4orm

This paper investigates how diffusion generative models leverage (unknown) low-dimensional structure to accelerate sampling. Focusing on two mainstream samplers -- the denoising diffusion implicit model (DDIM) and the denoising diffusion probabilistic model (DDPM), we prove that their iteration complexities under exact score functions are at most the order of $k/\varepsilon$ (up to log factor), where $\varepsilon$ is the precision in total variation distance and $k$ is some intrinsic dimension of the target distribution. We further extend these convergence guarantees to the setting in which the score functions are learned from data rather than known exactly, showing that the convergence performance degrades gracefully under suitable score estimation assumptions. We then show that these assumptions are attainable via kernel-based score estimators with finite-sample guarantees that also adapt to the low-dimensional structure. Our results apply to a broad family of target distributions without requiring smoothness or log-concavity. Our findings provide the first rigorous evidence for the adaptivity of the DDIM-type samplers to unknown low-dimensional structure, and improve over the state-of-the-art DDPM theory regarding total variation convergence.

As Classifier-Free Guidance (CFG) has proven effective in conditional diffusion model sampling for improved condition alignment, many applications use a negated CFG term as a Negative Prompting (NP) to filter out unwanted features from samples. However, simply negating CFG guidance creates an inverted probability distribution, often distorting samples away from the marginal distribution. Inspired by recent advances in conditional diffusion models for inverse problems, here we present a novel method to achieve guidance toward the given condition using contrastive loss. Specifically, our guidance term aligns or repels the denoising direction based on the given condition through contrastive loss, achieving a similar guiding effect to traditional CFG for positive conditions while overcoming the limitations of existing negative guidance methods. Experimental results demonstrate that our approach effectively injects or removes the given concepts while maintaining sample quality across diverse scenarios, from simple class conditions to complex and overlapping text prompts.

Synthetic Aperture Radar (SAR) imagery provides robust environmental and temporal coverage (e.g., during clouds, seasons, day-night cycles), yet its noise and unique structural patterns pose interpretation challenges, especially for non-experts. SAR-to-EO (Electro-Optical) image translation (SET) has emerged to make SAR images more perceptually interpretable. However, traditional approaches trained from scratch on limited SAR-EO datasets are prone to overfitting. To address these challenges, we introduce Confidence Diffusion for SAR-to-EO Translation, called C-DiffSET, a framework leveraging pretrained Latent Diffusion Model (LDM) extensively trained on natural images, thus enabling effective adaptation to the EO domain. Remarkably, we find that the pretrained VAE encoder aligns SAR and EO images in the same latent space, even with varying noise levels in SAR inputs. To further improve pixel-wise fidelity for SET, we propose a confidence-guided diffusion (C-Diff) loss that mitigates artifacts from temporal discrepancies, such as appearing or disappearing objects, thereby enhancing structural accuracy. C-DiffSET achieves state-of-the-art (SOTA) results on multiple datasets, significantly outperforming the very recent image-to-image translation methods and SET methods with large margins.

The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel intensities. The TV method has been widely applied in image processing and computer vision for its ability to preserve edges and enhance image quality. In this paper, we propose a Mixed-norm TV (MixTV) model for image denoising and the associated numerical algorithm to carry out the procedure, which is particularly effective in removing several types of noise and their combinations. Our MixTV admits a unique solution and the associated numerical algorithm guarantees convergence. Numerical experiments are demonstrated to show improved effectiveness and denoising quality compared to other TV models. Such encouraging results further enhance the utility of the TV method in image processing. Our project page is available at https://jing-en-huang.github.io/MixTV.

Detailed and photorealistic 3D human modeling is essential for various applications and has seen tremendous progress. However, full-body reconstruction from a monocular RGB image remains challenging due to the ill-posed nature of the problem and sophisticated clothing topology with self-occlusions. In this paper, we propose PSHuman, a novel framework that explicitly reconstructs human meshes utilizing priors from the multiview diffusion model. It is found that directly applying multiview diffusion on single-view human images leads to severe geometric distortions, especially on generated faces. To address it, we propose a cross-scale diffusion that models the joint probability distribution of global full-body shape and local facial characteristics, enabling detailed and identity-preserved novel-view generation without any geometric distortion. Moreover, to enhance cross-view body shape consistency of varied human poses, we condition the generative model on parametric models like SMPL-X, which provide body priors and prevent unnatural views inconsistent with human anatomy. Leveraging the generated multi-view normal and color images, we present SMPLX-initialized explicit human carving to recover realistic textured human meshes efficiently. Extensive experimental results and quantitative evaluations on CAPE and THuman2.1 datasets demonstrate PSHumans superiority in geometry details, texture fidelity, and generalization capability.

The imitation of cursive handwriting is mainly limited to generating handwritten words or lines. Multiple synthetic outputs must be stitched together to create paragraphs or whole pages, whereby consistency and layout information are lost. To close this gap, we propose a method for imitating handwriting at the paragraph level that also works for unseen writing styles. Therefore, we introduce a modified latent diffusion model that enriches the encoder-decoder mechanism with specialized loss functions that explicitly preserve the style and content. We enhance the attention mechanism of the diffusion model with adaptive 2D positional encoding and the conditioning mechanism to work with two modalities simultaneously: a style image and the target text. This significantly improves the realism of the generated handwriting. We set a new benchmark in our comprehensive evaluation, achieving 61 % mAP and 56 % top-1 accuracy in style preservation, significantly outperforming the previous best method (37 % mAP, 30 % top-1). We are making our code publicly available for reproducibility, supporting research in this area and research into potential countermeasures: https://github.com/M4rt1nM4yr/paragraph_handwriting_imitation_ldm

In this paper, we propose a novel locally statistical variational active contour model based on I-divergence-TV denoising model, which hybrides geodesic active contour (GAC) model with active contours without edges (ACWE) model, and can be used to segment images corrupted by multiplicative gamma noise. By adding a diffusion term into the level set evolution (LSE) equation of the proposed model, we construct a reaction-diffusion (RD) equation, which can gradually regularize the level set function (LSF) to be piecewise constant in each segment domain and gain the stable solution. We further transform the proposed model into a general ROF model by adding a proximity term ,and it can be solved by a fast denoising algorithm proposed by Jia-Zhao or soved by BM3D and NLM denoising algorithm, which also provide a unified solution framework for formally generalized-ROF-like subproblems arising in multivariate splitting algorithms.

In this paper, we propose a novel variational active contour model based on Aubert-Aujol (AA) denoising model, which hybrides geodesic active contour (GAC) model with active contours without edges (ACWE) model and can be used to segment images corrupted by multiplicative gamma noise. We transform the proposed model into classic ROF model by adding a proximity term.[26] was submitted on 29-Aug-2013, and our early edition was ever submitted to TGRS on 12-Jun-2012, Venkatakrishnan et al.[27] proposed their PnP algorithm on 29-May-2013, so Venkatakrishnan and we proposed the PnP algorithm almost simultaneously. Inspired by a fast denosing algorithm proposed by Jia-Zhao recently, we propose two fast fixed point algorithms to solve SAR image segmentation question.

In this paper, we propose a novel locally statistical active contour model (LACM) based on Aubert-Aujol (AA) denoising model and variational level set method, which can be used for SAR images segmentation with intensity inhomogeneity. Then we transform the proposed model into a global optimization model by using convex relaxation technique. Firstly, we apply the Split Bregman technique to transform the global optimization model into two alternating optimization processes of Shrink operator and Laplace operator, which is called SB_LACM model. Moreover, we propose two fast models to solve the global optimization model , which are more efficient than the SB_LACM model. The first model is: we add the proximal function to transform the global optimization model to a general ROF model[29], which can be solved by a fast denoising algorithm proposed by R.-Q.Jia, and H.Zhao; [29] was submitted on 29-Aug-2013, and our early edition was ever submitted to TGRS on 12-Jun-2012, Venkatakrishnan et al. [30] proposed their PnP algorithm on 29-May-2013, so Venkatakrishnan and we proposed the PnP algorithm almost simultaneously. Thus we obtain a fast segmentation algorithm with global optimization solver that does not involve partial differential equations or difference equation, and only need simple difference computation. The second model is: we use a different splitting approach than one model to transform the global optimization model into a differentiable term and a general ROF model term, which can be solved by the same technique as the first model.

Ranking generative models based on the fidelity and diversity of their outputs is required to identify the best generator in a group of candidate generative AI models. To rank a group of models in a conventional centralized setting, a standard score is commonly evaluated for each involved model. The selection and design of reference-based evaluation scores have been extensively studied in centralized settings, where the reference samples are drawn from a single probability distribution. However, in practical scenarios including distributed learning contexts, reference samples are distributed across multiple clients, each potentially with a heterogeneous data distribution. In this work, we investigate the ranking of generative models in such distributed settings with heterogeneous data distributions across clients. We focus on the widely used family of kernel distance (KD) evaluation metrics. We prove that, for every kernel function, ranking models by the averaged KD scores of individual clients yields the same ordering as a centralized KD evaluation using the combined reference data from all the clients. We further extend our analysis to other popular metrics, including the Fréchet Distance (FD), for which the individual client scores could be insufficient for accurate model ranking. We present the numerical results of several experiments on standard image datasets and generative models to validate our theoretical findings regarding distributed ranking using various evaluation scores.

Diffusion models have proven to be a flexible and effective framework for modelling probability distributions on finite-dimensional spaces. However, many physical modelling problems such as time series are naturally described over function spaces. In this work we apply diffusion models to such stochastic processes. To do so we consider a spectral representation of the data, obtained using a kernel, thereby dissociating the stochastic part of the processes from their space-time structure. As a result, the stochasticity of the processes is entirely encoded in the spectral coefficients, which we truncate and model using standard finite-dimensional diffusion models. By truncating the representation in the spectral domain we ensure our resulting model defines valid stochastic processes, thereby naturally satisfying consistency and exchangeability criteria. Projecting our spectral diffusion models back to the original input space, we show that for any given marginals our approach corresponds to a diffusion model with correlated noise, with explicit covariance matrix given by the kernel. We demonstrate our method's effectiveness for modelling various multimodal datasets as well as conditional sampling by amortising our models with respect to a context set.

In general, reliable communication via multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) requires accurate channel estimation at the receiver. The existing literature largely focuses on denoising methods for channel estimation that depend on either (i) channel analysis in the time-domain with prior channel knowledge or (ii) supervised learning techniques which require large pre-labeled datasets for training. To address these limitations, we present a frequency-domain denoising method based on a reinforcement learning framework that does not need a priori channel knowledge and pre-labeled data. Our methodology includes a new successive channel denoising process based on channel curvature computation, for which we obtain a channel curvature magnitude threshold to identify unreliable channel estimates. Based on this process, we formulate the denoising mechanism as a Markov decision process, where we define the actions through a geometry-based channel estimation update, and the reward function based on a policy that reduces mean squared error (MSE). We then resort to Q-learning to update the channel estimates. Numerical results verify that our denoising algorithm can successfully mitigate noise in channel estimates. In particular, our algorithm provides a significant improvement over the practical least squares (LS) estimation method and provides performance that approaches that of the ideal linear minimum mean square error (LMMSE) estimation with perfect knowledge of channel statistics.

Despite the empirical success of Diffusion Models (DMs) and Variational Autoencoders (VAEs), their generalization performance remains theoretically underexplored, especially lacking a full consideration of the shared encoder-generator structure. Leveraging recent information-theoretic tools, we propose a unified theoretical framework that provides guarantees for the generalization of both the encoder and generator by treating them as randomized mappings. This framework further enables (1) a refined analysis for VAEs, accounting for the generator's generalization, which was previously overlooked; (2) illustrating an explicit trade-off in generalization terms for DMs that depends on the diffusion time $T$; and (3) providing computable bounds for DMs based solely on the training data, allowing the selection of the optimal $T$ and the integration of such bounds into the optimization process to improve model performance. Empirical results on both synthetic and real datasets illustrate the validity of the proposed theory.

Recent work has popularized a practical recipe in diffusion and flow matching: predict the clean signal $x$, convert it to a velocity, and train through a velocity-space loss. The conversion contains a singular endpoint amplification and therefore appears prone to unstable optimization, yet recent systems obtain strong empirical results with this recipe. We investigate this tension through the integrability of the pre-optimizer stochastic-gradient second moment. Under stated initialization conditions, the moment diverges under Uniform sampling; boundary-suppressing sampling can restore integrability under an additional upper-growth condition. We then show that prediction--loss alignment eliminates this conversion-induced source of non-integrability. Under a uniform moment bound, alignment yields a finite second moment for every timestep density, including Uniform sampling. Controlled experiments across continuous and binary settings reproduce the predicted sampler-dependent instability and show that aligned objectives remain trainable across the tested samplers. These results reconcile pointwise amplification with sampler-dependent empirical success and support alignment as a principled route to more robust flow-matching training.

Latent generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals at a single, fixed complexity, governed by the latent dimensionality. This can be limiting: depending on the problem, a latent dimensionality that is too small may result in high representation error, while one that is too large may overfit to noise. We develop tunable latent priors for diffusion models, normalizing flows, and variational autoencoders, leveraging nested dropout. Across tasks including compressed sensing, inpainting, denoising, and phase retrieval, we show empirically that tunable priors consistently achieve lower reconstruction errors than fixed-complexity baselines. In the linear denoising setting, we derive the optimal complexity in closed form, showing how it depends on the noise level and the signal spectrum. This work demonstrates the potential of tunable latent generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.

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.

Diffusion models are increasingly used not only for sampling from learned data distributions, but also for generating samples that optimize task-specific objectives. A common approach is to guide the reverse diffusion process using gradients of an external objective. However, when the data distribution is supported on a structured feasible set, such as a manifold or a constraint set, gradient guidance can move samples away from the learned data geometry. In this paper, we study a simple projected-gradient-guided diffusion update based on the observation that the Stein denoising operator can act as an approximate projection onto the data geometry. The proposed update incorporates the objective gradient inside the denoising step, yielding an inference-time method that uses only a pretrained denoiser and gradient evaluations. We analyze this update as an inexact projected-gradient method for constrained optimization over learned feasible geometries. Our theory covers three settings: linear manifolds, compact convex feasible sets, and compact Riemannian submanifolds. In all these settings, we prove descent and finite-time convergence guarantees. Numerical experiments support the theoretical interpretation and illustrate how the proposed update balances objective descent with preservation of the learned geometry.

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.

The widespread adoption of encrypted traffic poses severe challenges to current security situational awareness systems based on network traffic monitoring. In existing dataset-driven training and testing studies, limitations such as shortcut learning induced by spurious feature correlations and sample imbalance caused by the long-tail distribution of real-world traffic result in weak generalization of traffic identification performance to real-world network traffic. To address these limitations, we propose TDDM-Melatt, a disentangled memory-based traffic classification framework with diffusion-based data augmentation. First, we design Melatt, a memory-decoupled traffic representation model, which employs Competitive Gating Long Short-Term Memory (CG-LSTM) to construct the encoder and decoder. We design a spurious-correlation-free pre-training and inference paradigm, employing strict topology anonymization and a frozen pre-trained encoder strategy to cut off the model's learning pathways for spurious features. During inference, classification is performed efficiently by a downstream classifier on the frozen representations. Second, we propose a Traffic Denoising Diffusion Model (TDDM) tailored to the characteristics of traffic data. Extensive experiments are conducted on 4 representative public benchmark datasets. Under strict flow-level splitting and anonymization, TDDM-Melatt outperforms 6 basic classification models and 6 SOTA representation learning models. The proposed method provides a new and effective technical pathway for encrypted traffic classification in real-world network environments.

Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables; consequently, similar activity can emerge from coordinated parameter changes. We formalize these compatible parameter sets as \emph{viable parameter manifolds}: the inverse images of target dynamical features under a parameter-to-feature map. The relevant codimension is not the number of reported features, but the effective rank of that map at the target scale. Locally redundant features lower the effective codimension, while poor conditioning, high curvature, or regime mixing degrade learnability. We train conditional score-based diffusion models on simulated parameter--feature pairs and use them as amortized samplers of prior-weighted viable sets. In the Lorenz system, scalar trajectory statistics generate thin viable sheets, and a finite-tolerance conditioning localizes a transition-adjacent corridor. In the Izhikevich neuron model, four firing descriptors lie close to a nearly two-dimensional family of features, and the learned inverse images reveal distinct regular and irregular compensation geometries. In a deterministic ODE reduction of finite spiking networks, the same framework reveals excitatory--inhibitory compensation, timescale--coupling tradeoffs, and viable manifolds across 4--12 parameter dimensions. In this view, robustness, compensation, and hidden parameter dependencies are organized as inverse geometry, with diffusion models providing practical tools for sampling, visualizing, and interrogating that geometry.

Reconstructing 3D geometry from 2D engineering line drawings is an inherently ambiguous problem: while visible strokes determine the object's projected structure, they do not specify the depth of each stroke. Rather than treating this problem as sketch-based asset generation, where models often infer unobserved structure, we study projection-faithful wireframe reconstruction: lifting a user-provided drawing into 3D according to its visible strokes. We formulate this task as conditional depth estimation over line drawings, predicting a depth value for each drawn pixel to produce a 3D wireframe. To model the ambiguities of orthographic projection, we implement a Latent Diffusion Model with spatial conditioning on the input sketch and optional partial-depth conditioning for iterative reconstruction. We train and evaluate our models on over three million synthetic image-depth pairs derived from CAD wireframes, including a newly curated corpus of roughly 90,000 shapes. Across varying shape complexities, our framework achieves robust reconstruction performance; scaling from 256 to 512 resolution with a retrained latent space roughly halves reconstruction error, reaching a 3.9% best-of-five (7.0% average) normalized depth error. These results demonstrate the potential of projection-faithful depth estimation as a user-controlled approach for iterative 3D wireframe creation in engineering design.