Denoising Diffusion Probabilistic Model

Selecting LoRA rank for diffusion fine-tuning requires balancing quality and compute cost. We present a controlled study on CIFAR-10 using a DDPM U-Net with ranks {2,4,8,16,32}, fixed optimization settings, and a reproducible local-folder pytorch-fid protocol. We report FID, trainable parameters, runtime, and GPU memory, then validate trends with extended-budget DDPM runs (20 epochs; ranks 4/8/16) and a Tiny DiT backbone (10 epochs; ranks 4/8/16). Results show moderate ranks are most efficient: rank 4 achieves the best DDPM FID (124.1380), rank 8 is close (124.2136), and higher ranks provide limited gains despite larger adaptation cost. These findings support small-to-moderate ranks as practical defaults under fixed training budgets.

Multivariate time series imputation (MTSI) aims to recover missing values in temporal data composed of multiple interdependent variables. This problem is central to real-world applications such as healthcare monitoring, traffic networks, and energy systems. Recent diffusion-based approaches have shown strong potential for probabilistic imputation by learning to generate missing values through iterative denoising. However, most existing approaches perform diffusion directly in the original data space, requiring the denoising network to simultaneously capture global structure, temporal dynamics, and stochastic variability. This makes the generative task unnecessarily complex, especially when modern deterministic imputers can already provide accurate initial reconstructions. To address this limitation, we propose RDDMPI, a conditional residual diffusion framework that operates directly in residual space. Instead of modeling the full missing signal directly, we reformulate probabilistic imputation as a baseline-residual decomposition, where a pretrained model captures the dominant signal and a diffusion process models the residual uncertainty. To better exploit deterministic guidance, \model{} conditions the reverse denoising process on both the baseline-completed signal and its latent representation, while a reliability-aware conditioning mechanism adaptively controls the influence of baseline information during residual generation. This formulation simplifies the diffusion learning objective, enabling it to focus on structured correction terms rather than reconstructing the full signal. Experiments on multiple benchmark datasets demonstrate that RDDMPI consistently improves both reconstruction accuracy and uncertainty quantification.

Denoising Diffusion Probabilistic Models (DDPMs) generate samples by starting from noise and repeatedly denoising while keeping each update close to the current noisy state. This behavior is effective in many continuous domains, but its role is less clear for globally constrained discrete tasks, such as Sudoku, graph connectivity, Latin squares, and N-queens. In such settings, early discrete errors can be difficult to undo. As a result, standard diffusion sampling may preserve early mistakes, even when the model's clean predictions are informative. We compare standard samplers to sampling directly from the model's clean prediction. Without retraining, this single change improves Sudoku validity from 31% to 95%, with consistent gains across the other discrete tasks. We hypothesize that staying close to the current noisy state is harmful because the reverse trajectory can drift off the forward noising distribution the model was trained on. To reduce this train-test mismatch, we further introduce self-correction training, which exposes the model to its own predictions, improving robustness to errors that arise during inference. This substantially improves the performance of standard samplers. Our results suggest that continuous diffusion models can learn nontrivial global constraints, but discrete reasoning tasks require better alignment between training and inference: either through samplers that reduce commitment to early decisions, or through training that teaches the model to correct its own inference-time errors.

Diffusion models and recursive reasoners are both iterative, but they carry information across iterations differently. We add a persistent hidden state to a diffusion denoiser and remove its timestep conditioning, leaving a single shared update that can be run to arbitrary depth. The result is an anytime solver: accuracy keeps improving with inference depth far beyond the rollout lengths and backpropagation window used in training, reaching 99.90% exact solve on Sudoku-Extreme. We also obtain 98.93% solve rate on Maze-Unique. Surprisingly, progressive denoising is unnecessary at inference: holding corruption at its maximum by replacing every non-clue variable with fresh Gaussian noise at each step retains near-perfect solving and converges to stable solutions. This simple noise-injection mechanism enables a single trajectory to efficiently explore the solution space and settle on the correct answer without parallel rollouts, candidate selection, or external verifiers required by prior reasoning models. Nonetheless, ordered annealed corruption remains critical during training, which suggests that diffusion's primary contribution to our anytime solver is not a sampling procedure at inference, but a denoising training curriculum.

Denoising diffusion models are the dominant architecture for image generation, whereas most natural language generation and modeling are primarily handled by well-known transformer architectures employing attention mechanism. Here, we show that diffusion models also inherently use an attention mechanism very similar to that of transformers. Therefore, attention emerges as a universal machine learning principle, based on a general training objective. We also show similarities in basic functional principle of auto-encoders and attention-based models. These equivalences allows us to interchange these designs based on practical requirements. As an example, we can reformulate the diffusion framework to reduce the lengthy training process and computation-intensive image generation. Using this approach, a simplified algorithm is proposed for image generation which is based on attention mechanism. Results show that the attention-based implementation achieves comparable performance with significantly less effort and computational resources.

This work shows that diffusion models learned with standard denoising loss can provide effective global MCMC proposals for complex high-dimensional target densities. The method is motivated by the observation that sequentially applying a forward and reverse diffusion process defines a Markov chain with a target stationary distribution for an ideal denoiser trained on samples of the target distribution. This observation can be made exact for any denoiser by applying a Metropolis-Hastings step whose acceptance ratio includes the density of the forward and reverse paths of a discrete time SDE approximation. We therefore propose to train denoising diffusion models on locally convergent MALA samples to learn global MCMC proposals. We call the composition of the global denoiser-based path sampler and a local MALA sampler Denoising Diffusion Monte Carlo (DDMC). Experiments show that DDMC can provide global proposals with high acceptance across a variety of complex target densities. Our results offer preliminary evidence that the established scaling behavior of standard diffusion training transfers directly to exact sampling from high-dimensional unnormalized densities.

Automating empirical research is a long-standing direction of AI. Recent automatic research (AutoResearch) agents bring this goal within reach, as modern LLMs show the capability to independently implement solutions and learn from the execution outcomes. Behind these gains, post-training (especially RL) plays a central role. In this paper, we identify a fundamental tension when scaling RL for these agents: the two components of every AutoResearch trajectory (agent generation and environment execution) scale in very different manners, since all generation shares compute through batching, while each execution occupies its exclusive sandbox and real machine time. As a result, the environment execution dominates the training cost and becomes the bottleneck as trajectories grow. To resolve this tension, we propose World Model RL (WMRL), which replaces environment execution with a world model to remove this bottleneck. Additionally, the world model can be imperfect, as its rewards are corrupted by bias and noise. Therefore, we further equip WMRL with two mitigations, Online Debiasing and Inverse-Variance Denoising, which offset the bias and suppress the noise respectively. Theoretically, we prove that both mitigations of WMRL strictly improve the convergence guarantee. Empirically, WMRL accelerates training by 3-4x on various tasks at different agent scales, while exceeding the performance of standard RL baselines. Moreover, our post-trained 4B and 9B agents outperform much larger open-weight agents of 48B and 120B on held-out benchmarks. Beyond AutoResearch, WMRL also transfers to post-training embodied VLA policies, which demonstrates the generalizability of our method.

Diffusion bridge models leverage Doob's $h$-transform to construct stochastic transports between arbitrary endpoint distributions, and have shown strong potential in image-to-image translation and restoration. However, most existing bridge models rely on hard endpoint conditioning, which forces the terminal state to match a prescribed target exactly. This hard constraint induces terminal-boundary singularities: the terminal law collapses to a Dirac measure, and the resulting drift coefficients become ill-conditioned near the endpoint. In this paper, we propose Soft Denoising Diffusion Bridge Models (SDDBMs), a generalized framework that regularizes diffusion bridges directly at the level of their terminal constraints. Instead of imposing an exact endpoint, SDDBMs prescribe a non-degenerate Gaussian terminal marginal under the transformed path measure, with a flexible terminal center and variance. Starting from this prescribed marginal, we develop a complete closed-form construction of the soft bridge, including the Gaussian terminal reweighting and soft $h$-function, the induced Gaussian forward marginals and $\mathbf{x}_0$-free dynamics. Theoretically, SDDBMs provide a unified probabilistic perspective that encompasses existing diffusion bridge models, including DDBMs, GOUB, and UniDB, as special cases under specific parameter choices. Extensive experiments on image restoration tasks demonstrate that SDDBMs achieve improved numerical stability and superior generation quality over existing bridge-based methods.

Player-centric ball action spotting requires temporally precise event detection together with actor attribution in crowded, partially observed multi-agent sports videos. Existing Denoising Sequence Transduction (DST) baselines treat the player-role dimension as part of a flattened frame-level representation, which weakens the inductive bias for modeling player-specific temporal evolution and inter-player interactions. To address this limitation, we propose Multi-Entity Denoising Sequence Transduction (ME-DST). ME-DST keeps the role-slot dimension throughout encoding. It uses temporal attention to model the history of each role slot, and spatial attention to exchange information across role slots at each frame. This factorized design gives the model a direct structure for separating within-player evolution from inter-player context. We also add learnable role embeddings, tracking-derived tactical features, and fused visual predictions from X3D-L and Swin3D-S. Experiments on the FOOTPASS dataset show that ME-DST reaches a Micro F1 of 0.778. This improves the strongest official TAAD+DST baseline by 10.3 percentage points. Controlled ablations show that preserving the entity axis and encoding role identity are central to this gain. These results suggest that explicit entity modeling is an effective inductive bias for player-centric sports event understanding.

Single-image self-supervised denoising replaces unavailable clean targets with surrogate targets constructed from noisy observations. Its effectiveness therefore depends on how closely the surrogate objective remains aligned with supervised denoising, especially when noise is correlated, spatially nonstationary, or unknown. We express the discrepancy between a broad class of MSE-based self-supervised objectives and supervised MSE as a parameter-independent constant and a trace interaction between the surrogate-target residual and the prediction error. The corresponding gradient discrepancy is determined by the gradient of this interaction. This formulation provides a common view of paired-noise, blind-spot, weak-noise, re-corruption, and sub-image methods, while revealing that a small global interaction may conceal substantial positive and negative regional interactions through spatial cancellation. Building on these observations, we propose LoTA-N2N, a two-stage zero-shot adaptation framework. Stage 1 trains a denoiser on complementary sub-image pairs and freezes it to construct detached clean-sub-image proxies. Stage 2 estimates the residual--prediction interaction using these proxies and suppresses its patch-wise absolute magnitude. We show that the local construction prevents spatial cancellation and upper-bounds the magnitude of the corresponding global interaction. Experiments across natural, confocal, and X-ray images, complemented by iteration-matched controls, controlled noise shifts, and gradient diagnostics, show consistent gains over MSE-only adaptation under IID, spatially varying, and mixed noise. Overall, LoTA-N2N demonstrates that estimated local interaction and spatial cancellation control provide effective design principles for single-image self-supervised denoising without paired clean targets, repeated acquisitions, or a predefined re-corruption model.

Multiplicative Gamma noise is a signal-dependent degradation in coherent imaging; synthetic aperture radar (SAR) despeckling is its most prominent real-world instance. Existing diffusion denoisers parameterize their forward process by abstract signal-to-noise schedules rather than by the physical look number $L$, so different deployment scenarios typically require separately trained models, and transfer from synthetic Gamma training to real SAR remains challenging without clean ground truth. We introduce $γ$-Bridge, a look-parametric bridge whose schedule $L(t)$ connects the noisy observation at $L_{obs}$ to the clean limit through exact multiplicative Gamma marginals. Its closed-form Gamma--Lévy reverse posterior admits both stochastic and deterministic processes, while observation conditioning and a two-step consistency loss stabilize multi-step inference in the low-SNR single-look regime. Because bridge time directly represents $L$, one conditioned network can smart-start from any admissible input look and stop at a target look number. These two orthogonal controls enable zero-shot restoration over the full admissible grid after training only at $L_{obs} = 1$ on natural images with synthetic Gamma corruption. Combined with a homogeneous-patch look estimator, $γ$-Bridge processes data from six spaceborne and airborne SAR sensors without sensor-specific fine-tuning, achieving leading results on standard synthetic benchmarks while providing physically interpretable input and output controls absent from prior denoisers. Codes are released \href{https://github.com/Teriri1999/GammaBridge}{here}.

Machine learning models for system diagnostics rely on kernel execution traces to capture fine-grained system behavior, but collecting production traces in industrial systems is costly due to runtime overhead, storage demands, and privacy constraints. We present TraceSynth, a diffusion-based framework for generating synthetic kernel traces that augment limited real data for downstream ML tasks. TraceSynth models traces as multi-channel sequences (event types, timestamps, CPU affinity, thread identifiers, and process metadata) using a Transformer-based denoising diffusion process with constraint-guided repair to enforce system invariants. Across six benchmarks, results show strong workload dependence. For deterministic, compute-heavy workloads (scimark2), synthetic augmentation achieves 87.2% F1-Macro at context length L=4096, only 2.6 percentage points below real-only baselines. Context length is the dominant quality factor, with L=4096 yielding a +104% relative improvement over L=256, while constraint-guided repair improves synthetic data quality by up to 4.3%. Ablation studies show that lightweight 2-channel models retain 97-99% of the performance of full 6-channel models at roughly half the computational cost. TraceSynth supports cost-effective augmentation of kernel execution traces in production observability pipelines and helps identify when synthetic data can substitute for limited real traces.

Text-to-image diffusion models exhibit unprecedented generative capability and contain rich intermediate representations that can be useful for discriminative vision tasks. Motivated by this observation, we study a focused question: how can the denoising dynamics of a pretrained diffusion model be adapted to support discriminative representation learning while preserving its generative behavior under parameter-efficient updates? We present D$^3$CL as an investigation of this question. Our key observation is that noisy latents at different diffusion timesteps can be interpreted as stochastic views of the same underlying image, enabling a contrastive objective to be coupled with the standard denoising reconstruction loss. This formulation provides a simple way to probe the interaction between generative denoising and discriminative representation learning without training from scratch. To keep the adaptation lightweight, we apply LoRA updates to a pretrained Stable Diffusion backbone while freezing the original model parameters. D$^3$CL provides strong empirical evidence that reconstruction and noise-level contrastive objectives can be complementary: on ImageNet-1K, it obtains 80.1% linear-probing accuracy and an FID of 5.56 for $256 \times 256$ unconditional generation. Additional ablations on the design space suggest that the usefulness of diffusion features depends on where and how denoising states are sampled. These results establish D$^3$CL as a parameter-efficient adaptation framework for pretrained diffusion models, showing that noise-level contrastive learning can structure denoising representations for discriminative tasks while maintaining generative performance.

Positron emission tomography (PET) seeks to balance diagnostic quality with ra-diation dose. Low-count PET noise is non-Gaussian, non-stationary, and spatial-ly dependent. It scales directly with local activity and is shaped by iterative recon-struction and physical corrections. Standard denoising diffusion probabilistic models (DDPMs) ignore these PET properties. Their forward process adds iso-tropic, homoscedastic Gaussian noise to the target. Such an approach fails to cap-ture the realistic physical degradation generated by the imaging system. To ad-dress the above limitations, this study introduces a heteroscedastic residual diffu-sion model (HDDPM) for low-count brain PET recovery in which the forward corruption is itself intensity-aware. We designed a fixed, Poisson-based variance module to generate voxel-wise noise maps. These maps naturally place stronger noise perturbation on low-activity regions than high-activity ones, meanwhile the network predicts the low-to-standard-count residual under explicit dose-fraction conditioning. We evaluated our proposed model (HDDPM) alongside generative frameworks across three different scanners, using both internal and external da-tasets at various simulated dose levels (1% to 50%). HDDPM and isotropic DDPM showed comparable overall image quality, but HDDPM stood out in the lowest-dose (1%) external scans. It is highly reliable and significantly reduces measurement errors in both high- and low-activity regions, compared to the standard model. These results support that heteroscedastic noising with the pro-posed HDDPM is feasible, and it provides a physically motivated inductive bias for quantitative low-count PET recovery by reflecting the activity-dependent noise structure of PET.

Diffusion language models offer a promising alternative to autoregressive models due to their potential for parallel and iterative generation. However, existing approaches use a single network for both context representation and iterative denoising, forcing one model to serve both roles and limiting its capacity for either role. We propose TwoTower, a block-wise autoregressive diffusion model that decouples these roles into two towers: a frozen AR context tower that causally processes clean tokens, and a trainable diffusion denoiser tower with bidirectional block attention that refines noisy blocks via cross-attention to the context. Built on Nemotron-3-Nano-30B-A3B, an open-weight 30B hybrid Mamba-Transformer MoE model, and trained on approximately 2.1T tokens, Nemotron-Labs-TwoTower retains 98.7% of the autoregressive baseline's quality while offering 2.42X higher wall-clock generation throughput. We release the code and model weights at https://huggingface.co/collections/nvidia/nemotron-labs-twotower.

Advanced semiconductor nodes drastically increased demand for Transmission Electron Microscopy (TEM), yet destructive sample preparation, slow imaging and high costs severely limit the availability of diverse datasets needed for downstream machine learning (ML). Synthetic data generation is becoming essential, but current generative models often miss TEM-specific noise, structural detail, and stochastic variability crucial for evaluation. We present a Denoising Diffusion Probabilistic Model (DDPM) framework for synthetic TEM image generation under extreme data scarcity. A progressive patch-based training strategy scales from low-resolution patches to full images, enabling from-scratch training with only 15 samples. We integrate a custom TrivialAugment adaptation, cross-process domain transfer, classifier guidance, and RePaint-style inpainting, culminating in full-image generation that preserves global structural and spatial relationships in compliance with FAB metrology requirements. Beyond synthesis, we repurpose DDPM feature representations for segmentation, partitioning encoder feature maps to obtain coherent region masks. Our synthetic images achieve up to MS-SSIM > 0.98 and qualitative expert assessment consistent with structural similarity results, facilitating downstream ML training for defect detection, segmentation, and metrology while preserving statistical and physical realism.

Neighboring-slice self-supervised denoising is attractive for volumetric medical imaging, yet inter-slice misalignment breaks anatomical correspondence and often yields ghosting and blurred margins when adjacent slices are used naively as targets. We propose Neighbor-Guided Patch Sampling (NGPS), a lightweight framework that constructs neighboring supervision under local inter-slice misalignment without explicit registration. To avoid learning from misleading targets, prior methods commonly mask discrepant regions, but this stabilizes training at the cost of leaving a non-trivial portion of neighboring evidence unexploited, particularly around high-frequency anatomical boundaries. NGPS addresses this by decoupling structure matching from signal retrieval: for each masked location, it searches a local neighborhood for structurally similar candidate patches using a simple guide image (e.g., fast bilateral filtering), while retrieving the supervision signal directly from the raw noisy neighbor at the matched coordinates. By matching on a noise-attenuated guide while retrieving raw values from neighboring slices, NGPS constructs local pseudo targets without a learned registration module. Across the evaluated CT and synthetic-Rician MRI settings, NGPS improves fidelity and structure-sensitive metrics. Code is available at https://github.com/cv-cho/NGPS .

Text-guided Open-vocabulary Object Counting (TOOC) enables counting arbitrary object categories specified by text prompts, offering substantially greater flexibility than conventional closed-set counting. However, existing TOOC methods are developed and evaluated primarily on ideal images, while real-world scenes often suffer from adverse conditions such as rain, fog, darkness, and sensor noise, which severely degrade visual quality and impair vision-language alignment. To bridge this gap, we introduce Robust-TOOC, the first benchmark for evaluating TOOC under diverse corruption conditions, which covers six representative degradation types: rain, fog, darkness, Gaussian noise, salt-and-pepper noise, and mixed corruption. To improve robustness while preserving the original counting architecture, we propose Dual-TTT, a dual-architecture test-time training framework for TOOC. Specifically, during test-time training, Dual-TTT updates only the Text-guided Lightweight Denoising module (TL-Denoiser), while keeping the original counting network frozen. Inspired by diffusion models, the TL-Denoiser is optimized to remove corruption-aware noise from image representations under degraded conditions. Since only the TL-Denoiser is trained at test time, Dual-TTT is annotation-free and can be seamlessly integrated into existing TOOC models without modifying their original architecture. Extensive experiments on multiple recent TOOC baselines demonstrate the effectiveness of our method.

Inverse rendering of urban scenes from captured videos enables numerous applications, including content creation and autonomous driving simulation. Physically-based rendering methods follow and control lighting physics, but suffer from reconstruction and rendering artifacts. While generative models produce realistic videos, they offer limited consistency and controllability. We present BRDFusion, a unified framework that combines two complementary models for inverse and forward rendering. Specifically, BRDFusion recovers explicit, consistent scene properties with physical modeling and alleviates optimization ambiguity with generative priors. During forward rendering, the physical model provides controllable rendering from the scene configuration, and the generative model denoises and fixes artifacts. Therefore, our method produces high-quality videos while allowing precise control, outperforming baselines in real and synthetic scenes. Moreover, BRDFusion supports novel-view relighting, night simulation, and dynamic object insertion/editing. Project page: https://shigon255.github.io/brdfusion-page/

Insertion Language Models (ILMs) offer several advantages over left-to-right generation and mask-based generation. However, existing formulations of insertion-based generation have largely been ad-hoc. In this paper, we derive a diffusion-style denoising objective for ILMs from first principles by formulating the noising process as a continuous-time Markov chain on the space of variable-length sequences. We show that previous formulations of ILMs can be viewed as special cases of this denoising framework. Through empirical evaluation on a synthetic planning task, we show that the proposed approach retains the benefits of insertion-based generation over left-to-right generation and masked diffusion models. In language modeling, our diffusion-based approach is competitive with left-to-right generation and masked diffusion models, while offering additional flexibility in sampling compared to existing insertion language models.

Lossy text compression reduces data size while preserving core meaning, making it well-suited for summarization, automated analysis, and digital archives. Despite the dominance of transformer-based models in language modeling, integrating context vectors and entropy coding into Sequence-to-Sequence (Seq2Seq) generation remains underexplored. A key challenge lies in identifying the most informative context vectors from encoder output and incorporating entropy coding to enhance storage efficiency while maintaining high-quality outputs, even under noisy text. We introduce TextEconomizer, an encoder-decoder framework paired with a transformer neural network that reduces variable-sized inputs by 50% to 80% without prior knowledge of dataset dimensions. Our model achieves competitive compression ratios via entropy coding while delivering near-perfect text quality, assessed by BLEU, ROUGE, METEOR, and semantic similarity scores. TextEconomizer operates with approximately 153x fewer parameters than comparable models, achieving a 5.39x compression ratio without sacrificing semantic quality. We also evaluate an LSTM-based autoencoder achieving a state-of-the-art 67x compression ratio with 196x fewer parameters, and LLaMAFormer, a modified transformer with 263x fewer parameters than ICAE while maintaining competitive text quality. TextEconomizer significantly surpasses existing transformer-based models in balancing memory efficiency and high-fidelity outputs, marking a breakthrough in lossy compression with optimal space utilization.

Lossless pixel-level image transmission is a fundamental regime beyond semantic communications, because exact recovery requires both accurate symbol probability modeling and reliable delivery over noisy channels. This paper proposes DDM-SSCC, a discrete-diffusion-model-based separate source-channel coding framework for lossless image transmission. Different from raster-order autoregressive coding, the proposed source codec adapts a diffusion language model to pixel-token restoration and performs synchronized reverse arithmetic coding under bidirectional attention, allowing multiple masked tokens to be coded within one reverse denoising step. This progressive restoration process also yields a more favorable source representation for noisy transmission, since newly restored tokens can serve as bidirectional context in subsequent denoising steps. To bridge the gap between generation-oriented masked denoising and lossless arithmetic coding, we further introduce a Halton-guided denoising order, a mask-ratio-aware cosine schedule, and a lightweight temperature calibration module. These designs respectively improve spatial coverage, adapt the denoising pace to context reliability, and calibrate the probability tables used by arithmetic coding. Experiments on CIFAR10, DIV2K-LR-X4, and Kodak over additive white Gaussian noise and Rayleigh fading channels show that DDM-SSCC achieves better exact-recovery performance than representative lossless and semantic communication baselines, while ablation studies verify the effectiveness of the proposed denoising order, schedule, and calibration modules.

Modern video diffusion models generate increasingly realistic and temporally coherent videos, motivating their use as candidate world simulators. Yet it remains unclear whether these models internally encode physical structure, or merely reproduce motion patterns seen during training. We study this question by probing video diffusion models along latent trajectories corresponding to real videos with known physical plausibility. To obtain such trajectories, we approximately invert the deterministic sampling process by integrating the learned velocity field backward from a clean video latent to noise, giving access to the model's intermediate states and attention maps. Using these recovered trajectories, we show that physical plausibility is linearly decodable from diffusion transformer states across IntPhys and InfLevel, reaching around 81.27% average accuracy and outperforming dedicated representation-learning baselines such as V-JEPA and VideoMAE. Surprisingly, this signal is absent from the VAE latent input and emerges inside the denoising transformer itself, despite the model not being trained with a self-supervised predictive objective. These findings suggest that physically meaningful representations can arise as a byproduct of generative denoising.

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

We propose Decoupled Residual Denoising Diffusion models (DRDD) for unified and data-efficient image-to-image (I2I) translation. While diffusion models have advanced I2I translation in terms of quality and diversity, we uncover a previously under-explored property in diffusion models. Crucially, beyond its conventional role of manifold lifting (i.e., moving data off low-dimensional manifolds), injecting Gaussian noise facilitates domain harmonization by implicitly aligning feature distributions across domains, a property particularly advantageous for unified I2I translation. However, existing diffusion models prematurely erode this harmonization effect, as noise and residuals are simultaneously removed in a single coupled diffusion process. To address this, DRDD decouples the diffusion process into two sequential and independent diffusion stages: (1) a stochastic noise diffusion for domain harmonization and manifold lifting, and (2) a deterministic residual diffusion that learns the core semantic mapping entirely within the fixed-noise domain. This decoupling preserves harmonization and manifold lifting effects throughout the transformation, substantially simplifying the learning of unified mappings across diverse tasks and domains. Notably, the noise diffusion stage is trained exclusively on abundant, unpaired target-domain images, greatly improving data efficiency. Comprehensive theoretical and empirical analysis demonstrates that DRDD is broadly compatible with mainstream diffusion models and consistently delivers robust, unified I2I translation, even under limited paired data. Our code is available at https://github.com/HKU-HealthAI/DRDD.

Real-world image restoration (IR) is bottlenecked by the scarcity of high-quality paired training data. Synthetic datasets are abundant but often fail to model real-world degradations, while real-world paired datasets are expensive and difficult to capture. As a result, IR models trained on these datasets show limited generalization in real-world scenarios. In this work, we propose Generative Ground Truth (GGT) by using generative multimodal foundation models (MFMs) to produce high-quality (HQ) targets from real-world low-quality (LQ) images. We first conduct a systematic evaluation of nine state-of-the-art MFMs, including Nano-Banana-2 and GPT-Image-2, on images of various scenes and degradation types. The results demonstrate that Nano-Banana-2 with VLM-based adaptive prompting shows the highest capability to synthesize perceptually realistic and content-faithful HQ targets, which can serve as the GGT for the LQ input. We then employ Nano-Banana-2 to build a GGT synthesis pipeline, which involves multi-stage quality control to ensure data reliability, and construct GGT-100K, an LQ-HQ paired dataset comprising 103,707 training pairs and covering diverse scenes and complex real-world degradations. A test set of 500 image pairs is also established. Extensive experiments show that GGT-100K consistently improves the real-world generalization of a wide range of IR models, with particularly strong benefits for finetuning generative models for IR tasks. Our results suggest that MFMs can serve as practical tools for restoration-oriented data generation, and GGT-100K is a useful resource to expand the generalization boundaries of real-world IR models.

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

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

This paper studies sampling error bounds for denoising diffusion probabilistic models (DDPMs) in the 2-Wasserstein distance. Our contributions are threefold. (i) Under general Lipschitz-type conditions on the score function and for a broad class of variance schedules, including the cosine schedule, we establish sharp upper bounds that are optimal in both the dimension and the number of steps, and recover several sharp error bounds previously obtained in the literature. (ii) We prove that the same Lipschitz-type conditions, which encompass those commonly imposed on the (learned) score, imply a logarithmic Sobolev inequality and hence a quadratic transportation cost inequality for the DDPM. As a consequence, in settings covered by existing work, an optimal Wasserstein bound, up to a logarithmic factor, follows from the recently obtained sharp error bound in the Kullback-Leibler divergence under geometric-type variance schedules. (iii) We show that for general log-concave target distributions, the optimal Wasserstein error bound remains attainable even without a quadratic transportation cost inequality for the target. Our analysis is based on viewing the DDPM sampler as a discretization of the Föllmer process rather than the conventional reverse Ornstein-Uhlenbeck process.

The Föllmer process is a Brownian motion conditioned to have a pre-specified distribution at time 1. This process can be interpreted as an ``augmented'' time-compressed version of the reverse stochastic differential equation (SDE) corresponding to the denoising diffusion probabilistic model (DDPM). While this fact has been indirectly used to analyze DDPM sampling errors via discretization of the reverse SDE, the connection between direct discretization of the Föllmer process and the DDPM sampler has not yet been fully explored. This paper clarifies this point while surveying relevant results from the literature. We show that discretized Föllmer processes give natural hyper-parameter settings of the DDPM sampler while accommodating a broader class of variance schedules than discretized reverse SDEs. Moreover, this allows us to systematically recover state-of-the-art results on DDPM sampling error bounds, along with slight improvements.

Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely on likelihood approximations that introduce sampling biases. We address these challenges by introducing a new energy-based model trained for denoising with a covariance-based regularization term that enforces consistency across different measurement conditions. The trained model can compute normalized posterior densities for diverse linear inverse problems, without additional retraining or fine tuning. In addition to preserving the sampling capabilities of diffusion models, this enables previously unavailable capabilities: energy-guided adaptive sampling that adjusts schedules on-the-fly, unbiased Metropolis-Hastings correction steps, and blind estimation of the degradation operator via Bayes rule. We validate the method on multiple datasets (ImageNet, CelebA, AFHQ) and tasks (inpainting, deblurring), demonstrating competitive or superior performance to established baselines.

Discrete diffusion language models improve generation efficiency through parallel token prediction, but standard $X_0$ prediction methods introduce factorization errors by approximating the clean token posterior with independent token-wise distributions. This paper proposes Factorization-Error-Free Discrete Diffusion Language Modeling (FeF-DLLM), which replaces independent clean-token prediction with an exact prefix-conditioned factorization of the clean posterior to better preserve token dependencies. To reduce the sequential cost introduced by prefix conditioning, FeF-DLLM further incorporates speculative decoding within diffusion denoising, accelerating inference while maintaining the parallel prediction and re-masking properties of DLLMs. Theoretically, we prove that FeF-DLLM generates from the true joint distribution and derive its expected acceleration ratio. Experiments on GSM8K, MATH, HumanEval, and MBPP demonstrate that our method improves accuracy by an average of 5.04 percentage points while achieving an average inference speedup of $3.86\times$.

Diffusion models generate samples by iteratively denoising a Gaussian prior, traversing a sequence of noise levels that, in every published sampler, decreases monotonically. Six years of intensive work has refined nearly every aspect of this recipe, including the corruption operator, the training objective, the schedule shape, the architecture, and the ODE solver. Yet the assumption of monotonicity itself has never been systematically tested. Here we ask whether monotonic sampling is load-bearing or merely conventional. We design four families of structured nonmonotonic schedules and apply them to three architecturally distinct generative models, DDPM, EDM, and Flow Matching, across NFE budgets ranging from 10 to 200 function evaluations, plus a 42-cell hyperparameter ablation, on CIFAR-10. Across all 90 tested configurations, no tested nonmonotonic schedule improves on the monotonic baseline. The magnitude of the penalty, however, spans nearly three orders of magnitude: persistent and substantial in DDPM, intermediate in Flow Matching, and indistinguishable from zero in EDM. We show that this variation is not noise but a structural property of each trained denoiser, and we formalize it as the Schedule Sensitivity Coefficient, a cheap, architecture-agnostic diagnostic that provides evidence of non-convergence to the Bayes-optimal denoiser at the critical noise level. Our findings justify the field's tacit reliance on monotonic schedules and supply a new probe of diffusion model quality complementary to sample-quality metrics such as Frechet Inception Distance.

Stable Diffusion (SD) has evolved DDPM (Denoising Diffusion Probabilistic Model) based image generation significantly by denoising in latent space instead of feature space. This popularized DDPM-based image generation as the cost and compute barrier was significantly lowered. However, these models could only generate fixed-resolution images according to their training configuration. When we attempt to generate higher resolutions, the resulting images show object duplication artifacts consistently. To solve this problem without finetuning SD models, recent works have tried dilating the convolution kernels of the models and have achieved a great level of success. But dilated kernels are harder to fine-tune due to being zero-gapped. Apart from this, other methods, such as patched diffusion, could not solve the object-duplication problem efficiently. Hence, to overcome the limitations of dilated convolutions, we propose kernel interpolation of SD models for higher-resolution image generation. In this work, we show mathematically that interpolation can correctly scale convolution kernels if multiplied by a constant coefficient and achieve competitive empirical results in generating beyond-training-resolution images with Stable Diffusion using zero training. Furthermore, we demonstrate that our method enables interpolation of deep neural networks to adapt to higher-dimensional training data, with a worst-case performance drop of $2.6\%$ in accuracy and F1-Score relative to the baseline. This shows the applicability of our method to be general, where we interpolate fully-connected layers, going beyond convolution layers. We also discuss how we can reduce the memory footprints of training neural networks, using our method up to at least $4\times$.

We theoretically study the hallucination phenomena in two canonical diffusion samplers: the stochastic Denoising Diffusion Probabilistic Model (DDPM) and the deterministic Denoising Diffusion Implicit Model (DDIM). We analyze the reverse ODE (DDIM) and SDE (DDPM) for a Gaussian mixture target, proving that after a critical time $τ$, (a) DDIM can become stuck on the segment connecting the two nearest modes and (b) DDPM stochasticity helps it become unstuck from this region, thus avoiding hallucination. Our empirical validation verifies that DDPM has a significantly lower hallucination rate than DDIM when this region is entered. Building on our observations, we exhibit how using additional stochastic steps can help DDIM avoid hallucinations and offer new insights on how to design improved samplers.

We propose a plug-and-play framework for speech enhancement and separation that augments predictive methods with a generative speech prior. Our approach, termed Stochastic Interpolant Prior for Speech (SIPS), builds on stochastic interpolants and leverages their flexibility to bridge predictive and generative modeling. Specifically, we decompose the interpolation dynamics into a task-specific drift and a stochastic denoising component, allowing a predictive estimate to be integrated directly into the generative sampling process. This results in a mathematically grounded framework for combining strong pretrained predictors with the expressive power of generative models. To this end, we train a score model using only clean speech, yielding a degradation-agnostic prior that can be reused across tasks. During inference, the predictor provides a deterministic drift that steers the sampling process toward a task-consistent estimate, while the score model preserves perceptual naturalness. Unlike prior hybrid approaches, which typically rely on architecture-specific conditioning and are tied to particular predictors or degradation settings, SIPS provides a unified framework that generalizes across predictors and additive degradation tasks. We demonstrate its effectiveness for both speech enhancement and speech separation using recent predictors such as SEMamba and FlexIO. The proposed method consistently improves perceptual quality, achieving gains up +1.0 NISQA for speech separation.

The performance of state-of-the-art object detectors degrades significantly under adverse weather, causing a safety-critical domain shift problem for autonomous vehicles. Recent efforts address this problem by relying on synthetic data to train the object detectors, which limits their real-world applicability. Meanwhile, pseudo-labeling is widely used for cross-dataset domain adaptation problems. However, these methods have not been exploited by weather-based domain adaptation approaches due to the noisy nature of such labels generated under harsh weather conditions. In this paper, we propose two new approaches to mitigate this weather-induced domain shift. First, we propose a Weather-Induced pseudo Label Denoising (WILD) framework that filters noisy pseudo labels generated by real data captured under adverse weather conditions. Second, we develop a novel hybrid training methodology, WILD SAM, that exploits both pseudo-label denoising and simulation-based training solutions while using real-data from the target harsh-weather domain. We validate both proposed approaches, WILD and WILD SAM, on the recently released Four Seasons dataset across rainy and snowy scenarios. Experiments show that the proposed frameworks improve Average Precision (AP) up to 13% and significantly reduce the weather-induced performance gap relative to the baseline. The code is available at: https://github.com/Kh-Hamed/WILD-SAM

In wireless communications, recovering the optimal solution to the multiple-input multiple-output (MIMO) detection problem is NP-hard. Obtaining high-quality suboptimal solutions with a favorable performance-complexity trade-off is particularly challenging in under-determined systems with $N_t$ transmit antennas and $N_r < N_t$ receive antennas. Recent diffusion-based MIMO detectors have shown promise, but they require extensive sampling iterations at inference time, and their performance degrades in under-determined scenarios. We propose GD4, a graph-based discrete denoising diffusion method for MIMO detection. Unlike existing diffusion-based detectors that operate in a continuous relaxed space, GD4 performs denoising directly in the discrete symbol space and enables fast inference with one or a few denoising evaluations. Numerical results show that, under a similar inference-time compute budget, GD4 produces higher-quality suboptimal solutions than existing diffusion-based detectors and some widely used classical baseline including box-constrained Babai point and the $K$-best box-constrained randomized Klein-Babai point in both under-determined and overdetermined settings.

Semantic segmentation and change detection are two fundamental challenges in remote sensing, requiring models to capture either spatial semantics or temporal differences from satellite imagery. Existing deep learning models often struggle with temporal inconsistencies or in capturing fine-grained spatial structures, require extensive pretraining, and offer limited interpretability - especially in real-world remote sensing scenarios. Recent advances in diffusion models show that Gaussian noise can be systematically leveraged to learn expressive data representations through denoising. Motivated by this, we investigate whether the noise process in diffusion models can be effectively utilized for discriminative tasks. We propose Noise2Map, a unified diffusion-based framework that repurposes the denoising process for fast, end-to-end discriminative learning. Unlike prior work that uses diffusion only for generation or feature extraction, Noise2Map directly predicts semantic or change maps using task-specific noise schedules and timestep conditioning, avoiding the costly sampling procedures of traditional diffusion models. The model is pretrained via self-supervised denoising and fine-tuned with supervision, enabling both interpretability and robustness. Our architecture supports both tasks (SS and CD) through a shared backbone and task-specific noise schedulers. Extensive evaluations on the SpaceNet7, WHU, and xView2 buildings damaged by wildfires datasets demonstrate that Noise2Map ranks on average 1st among seven models on semantic segmentation and 1st on change detection by a cross-dataset rank metric (average F1 primary, IoU tie-break). Ablation studies highlight the robustness of our model against different training noise schedulers and timestep control in the diffusion process, as well as the ability of the model to perform multi-task learning.

Graph few-shot learning, which focuses on effectively learning from only a small number of labeled nodes to quickly adapt to new tasks, has garnered significant research attention. Despite recent advances in graph few-shot learning that have demonstrated promising performance, existing methods still suffer from several key limitations. First, during the meta-training phase, these methods typically perform node representation learning in Euclidean space, which often fails to capture the inherently hierarchical structure existing in real-world graph data. Second, during the meta-testing phase, they usually fit an empirical target distribution derived from only a few support samples, even when this distribution significantly deviates from the true underlying distribution. To address these issues, we propose IMPRESS, a novel framework that IMproves graPh few-shot learning with hypeRbolic spacE and denoiSing diffuSion. Specifically, our model learns node representations in a hyperbolic space and enriches the support distribution through denoising diffusion mechanisms. Theoretically, IMPRESS achieves a tighter generalization bound. Empirically, IMPRESS consistently outperforms competitive baselines across multiple benchmark datasets.

Industrial surface defect detection often suffers from limited defect samples, severe long-tailed distributions, and difficulties in accurately localizing subtle defects under complex backgrounds. To address these challenges, this paper proposes an unsupervised defect detection method that integrates a Denoising Diffusion Probabilistic Model (DDPM) with an asymmetric teacher-student architecture. First, at the data level, the DDPM is trained solely on normal samples. By introducing constant-variance Gaussian perturbations and Perlin noise-based masks, high-fidelity and physically consistent defect samples along with pixel-level annotations are generated, effectively alleviating the data scarcity problem. Second, at the model level, an asymmetric dual-stream network is constructed. The teacher network provides stable representations of normal features, while the student network reconstructs normal patterns and amplifies discrepancies between normal and anomalous regions. Finally, a joint optimization strategy combining cosine similarity loss and pixel-wise segmentation supervision is adopted to achieve precise localization of subtle defects. Experimental results on the MVTecAD dataset show that the proposed method achieves 98.4% image-level AUROC and 98.3% pixel-level AUROC, significantly outperforming existing unsupervised and mainstream deep learning methods. The proposed approach does not require large amounts of real defect samples and enables accurate and robust industrial defect detection and localization. \keywords{Industrial defect detection \and diffusion models \and data generation \and teacher-student architecture \and pixel-level localization}

Open-Vocabulary Temporal Action Detection (OV-TAD) aims to localize and classify action segments of unseen categories in untrimmed videos, where effective alignment between action semantics and video representations is critical for accurate detection. However, existing methods struggle to mitigate the semantic imbalance between concise, abstract action labels and rich, complex video contents, inevitably introducing semantic noise and misleading cross-modal alignment. To address this challenge, we propose DFAlign, the first framework that leverages diffusion-based denoising to generate foreground knowledge for the guidance of action-video alignment. Following the 'conditioning, denoising and aligning' manner, we first introduce the Semantic-Unify Conditioning (SUC) module, which unifies action-shared and action-specific semantics as conditions for diffusion denoising. Then, the Background-Suppress Denoising (BSD) module generates foreground knowledge by progressively removing background redundancy from videos through denoising process. This foreground knowledge serves as effective intermediate semantic anchor between video and text representations, mitigating the semantic gap and enhancing the discriminability of action-relevant segments. Furthermore, we introduce the Foreground-Prompt Alignment (FPA) module to inject extracted foreground knowledge as prompt tokens into text representations, guiding model's attention towards action-relevant segments and enabling precise cross-modal alignment. Extensive experiments demonstrate that our method achieves state-of-the-art performance on two OV-TAD benchmarks. The code repository is provided as follows: https://anonymous.4open.science/r/Code-2114/.

Being one of the oldest and most basic problems in image processing, image denoising has seen a resurgence spurred by rapid advances in deep learning. Yet, most modern denoising architectures make limited use of the technical knowledge acquired researching the classical denoisers that came before the mainstream use of neural networks, instead relying on depth and large parameter counts. This poses a challenge not only for understanding the properties of such networks, but also for deploying them on real devices which may present resource constraints and diverse noise profiles. Tackling both issues, we propose an architecture dedicated to RAW-to-RAW denoising that incorporates the interpretable structure of classical self-similarity-based denoisers into a fully learnable neural network. Our design centers on a novel nonlocal block that parallels the established pipeline of neighbor matching, collaborative filtering and aggregation popularized by nonlocal patch-based methods, operating on learned multiscale feature representations. This built-in nonlocality efficiently expands the receptive field, sufficing a single block per scale with a moderate number of neighbors to obtain high-quality results. Training the network on a curated dataset with clean real RAW data and modeled synthetic noise while conditioning it on a noise level map yields a sensor-agnostic denoiser that generalizes effectively to unseen devices. Both quantitative and visual results on benchmarks and in-the-wild photographs position our method as a practical and interpretable solution for real-world RAW denoising, achieving results competitive with state-of-the-art convolutional and transformer-based denoisers while using significantly fewer parameters. The code is available at https://github.com/MIA-UIB/nonlocal-matchfilter .

Text-to-image generation powered by Diffusion Transformers (DiTs) has made remarkable strides, yet remote sensing (RS) synthesis lags behind due to two barriers: the absence of a domain-specialized DiT prior and the prohibitive cost of training at the large resolutions that RS applications demand. Training-free resolution promotion via Rotary Position Embedding (RoPE) rescaling offers a practical remedy, but every existing method applies a static positional scaling rule throughout the denoising process. This uniform compression is particularly harmful for RS imagery, whose substantially denser medium- and high-frequency energy encodes the fine structures critical for aerial-scene realism, such as vehicles, building contours, and road markings. Addressing both challenges requires a domain-specialized generative prior coupled with a denoising-aware positional adaptation strategy. To this end, we fine-tune FLUX on over 100,000 curated RS images to build a strong domain prior (RS-FLUX), and propose Spectrum-aware Highly-dynamic Adaptation for Resolution Promotion (SHARP), a training-free method that introduces a rational fractional time schedule k_rs(t) into RoPE. SHARP applies strong positional promotion during the early layout-formation stage and progressively relaxes it during detail recovery, aligning extrapolation strength with the frequency-progressive nature of diffusion denoising. Its resolution-agnostic formulation further enables robust multi-scale generation from a single set of hyperparameters. Extensive experiments across six square and rectangular resolutions show that SHARP consistently outperforms all training-free baselines on CLIP Score, Aesthetic Score, and HPSv2, with widening margins at more aggressive extrapolation factors and negligible computational overhead. Code and weights are available at https://github.com/bxuanz/SHARP.

Discrete graph generation has emerged as a powerful paradigm for modeling graph-structured data, yet state of the art models often rely on Graph Transformers or higher order architectures. We revisit this design assumption by introducing GenGNN, a modular message passing backbone for graph generation. GenGNN enables powerful generation by persisting edge fields through latent refinement of coupled node edge graph states, all without requiring global attention. Diffusion models integrating GenGNN achieve over 90 percent validity on standard benchmark datasets, performing within margins of Graph Transformer backbones and achieving up to 2x or even 5x faster inference. Systematic ablations isolate how GenGNN is resilient to oversmoothing during generative denoising, indicating each GenGNN component is necessary for downstream generation quality. Finally, representation-space analysis suggests GenGNN learns functionally similar representations to more theoretically-expressive architectures; even at deeper layers. As such, GenGNN uplifts local message-passing to challenge prevailing assumptions that performant discrete graph generation requires global attention or higher-order representations. Source Code Available Here

Diffusion models provide powerful generative priors for solving inverse problems by sampling from a posterior distribution conditioned on corrupted measurements. Existing methods primarily follow two paradigms: direct methods, which approximate the likelihood term, and proximal methods, which incorporate intermediate solutions satisfying measurement constraints into the sampling process. Under standard Gaussian approximations and locally-linear measurements, we demonstrate that these approaches differ fundamentally in their treatment of the diffusion denoiser's Jacobian within the likelihood term. While this Jacobian encodes critical prior knowledge of the data distribution, training-induced non-idealities can degrade performance in zero-shot settings. In this work, we bridge direct and proximal approaches by proposing a principled Jacobian-Aware Posterior Sampler (JAPS). JAPS leverages the Jacobian's prior knowledge while mitigating its detrimental effects through a corresponding proximal solution, requiring no additional computational cost. Additionally, we integrate our guidance into DDIM sampling, with a corrected conditional factor that has been missing in previous works. Our method enhances reconstruction quality across diverse linear and nonlinear noisy imaging tasks, outperforming existing diffusion-based baselines in perceptual quality while maintaining or improving distortion metrics.

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

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.

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.