Denoising

Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen. However, before any operator is applied, the grid has already determined how modeling capacity is allocated across space, resolution, and spectral bandwidth. We argue that this hidden design choice should itself be learnable, leading to a question different from standard operator learning: can a surrogate learn where resolution should exist before predicting field evolution? We formulate adaptive discretization as a physics-constrained conditional generation problem over valid mesh displacements. The success of diffusion models in PDE field prediction suggests their potential for learning adaptive discretizations under similar structured constraints. This leads to a two-stage diffusion framework: Stage 1 learns an r-adaptive displacement mesh conditioned on the observed dynamics, while Stage 2 predicts the solution evolution from the mesh-informed representation. The mesh generator is regularized by physics-aware proxy channels, geometric validity constraints, and local spectral concentration so that adaptation remains physically interpretable and numerically legal. Across five PDE regimes, the results show that diffusion-based learned discretization is competitive with adaptive-mesh and reduced-order baselines, with particularly strong gains in regimes where fixed or handcrafted allocation is insufficient. The main conclusion is not that there exists a universal optimal mesh rule, but that discretization should be learned in a regime-dependent manner: different spatial and spectral structures favor different allocation behaviors. This reframes adaptive meshing for neural PDE solvers from a solver-specific heuristic into a generative representation-learning problem.

Existing Stochastic 3D Human Motion Prediction models are fundamentally constrained by hard-coding the skeleton kinematics, severely limiting generalization, preventing cross-dataset training, and requiring complex data retargeting. We introduce EquiFusion, the first kinematics-agnostic model to solve this bottleneck, implementing a latent diffusion model with a permutation equivariant architecture. EquiFusion treats the kinematics' connectivity as an explicit input parameter, ensuring its internal computations are inherently agnostic to joint ordering and graph structure. This novel design enables truly cross-dataset generalization to unseen kinematics and unlocks novel zero-shot directions, such as motion prediction from partial or occluded observations and targeted limb generation. EquiFusion achieves state-of-the-art results on major benchmarks, being up to 75% more compact than previous kinematics-specific methods, while achieving faster training and inference. EquiFusion thus establishes a new, flexible standard for robust human motion prediction. Model and training code are available at https://ceveloper.github.io/publications/equifusion/.

Generative models often represent signals as dense grids of amplitudes, blurring sharp transients that are crucial for the correctness of physical signals. We introduce Singularity Space, a generative framework that represents signals through complex-plane singularities, rooted in the classical pole-residue representation of meromorphic functions. We learn a latent space of physically constrained, per-signal singularity configurations to solve an inverse problem from degraded or partial observations. The framework has three key properties: interpretability, in which each generated singularity configuration corresponds to a set of physical parameters; structural stability, which mitigates Gibbs artifacts at discontinuities; and resolution-free output reconstruction on arbitrary grids without retraining or interpolation. Our framework employs a transformer-based diffusion model that directly predicts samples at complex-plane singularity coordinates, subject to geometric constraints during sampling. As a controlled test case for sharp-feature recovery, we evaluate our framework on 1D Burgers shocks, where each shock is represented by 32 predicted singularities (an $8\times$ reduction versus a 1024-point grid signal). Our framework preserves signal structure ($\text{TV ratio} \approx 1$) under unseen test-time observation noise, achieves a $4.2\times$ lower reconstruction error in zero-shot sub-resolution generalization than a grid-based baseline, and recovers physical parameters to $10^{-4}$ absolute error in-distribution. These results suggest that singularity-based representations may provide a practical foundation for other transient-dominated signals such as speech and biomedical signals, with potential extension to higher-dimensional domains.

Diffusion models faithfully reproduce their training distribution, but also inherit its imbalances and leave rare or under-represented modes hard to reach. A natural inference-time remedy is to sample from the high-temperature target $p^{(γ)}_0(x) \propto p_0(x)^γ$ for $0 < γ< 1$, which flattens dominant modes and lifts rare ones. However, naive score scaling while correctly reweighting modes also inflates the per-mode variance, breaking the reverse diffusion process and degrading sample quality. We introduce variance-corrective time shifting, a training-free fix that queries the network at a shifted timestep and scales the resulting score by $γ$, canceling the variance inflation while preserving the mode reweighting. The correction turns simple temperature sampling into a practical diversity knob for pretrained diffusion and flow-matching backbones with no retraining, and we demonstrate consistent gains at minimal cost to sample quality and condition fidelity across DiT, Stable Diffusion and Motion Diffusion models. We further show that the timing of the temperature intervention enables coarse-to-fine control: high-noise stages drive compositional diversity across modes, while low-noise stages drive local appearance variation under a fixed composition.

AI models are increasingly trained on personal images scraped from social media and public platforms, often without consent, leading to serious privacy violations, such as unauthorized facial recognition and targeted advertising. To counter this, researchers have developed unlearnable examples (UEs), images modified with imperceptible noise to prevent AI models from extracting meaningful information. However, existing UE methods primarily rely on pixel-space noise, which can be bypassed by relearning strategies such as adversarial training, image transformation, and compression. While some techniques improve robustness, they often come at the expense of significant degradation in image utility and perceptual quality. In this paper, we introduce DiffUE to overcome these limitations by injecting noise into the semantic space of images instead of the pixel space. Instead of corrupting pixel values, DiffUE modifies high-level semantic features of images, ensuring robust unlearnability while preserving visual quality and utility. By leveraging a diffusion-based autoencoder framework to manipulate semantic features, DiffUE generates purposeful, natural-looking modifications that effectively resist advanced relearning strategies. Extensive experiments on four datasets, CIFAR-10, CIFAR-100, CelebA-HQ, and ImageNet, as well as a subjective user study, demonstrate that DiffUE significantly enhances the trade-off between image quality and unlearnability, offering a more robust and effective solution for safeguarding personal data in an increasingly exploitative AI landscape.

Open-vocabulary 3D scene understanding is commonly achieved by embedding 2D vision-language features such as CLIP into a 3D Gaussian Splatting scene, turning it into a text-queryable semantic field. However, attaching a high-dimensional feature to each of millions of Gaussians inflates a single scene to gigabytes, which makes storage and deployment the real bottleneck of these fields. Existing compact methods each learn and ship a per-scene codec, an autoencoder, a quantized codebook, or a distilled feature field, entangling field construction with field storage and never compressing the per-Gaussian assignment that holds the bulk of the cost. We argue that construction and storage should be decoupled, and that storage is a rate-distortion problem over the per-Gaussian binding to a small anchor table, a structure no prior open-vocabulary method compresses. We present CoSAG, which constructs the field without any per-scene training through a closed-form transmittance-weighted lift, spatially grounded semantic anchors, and multi-view denoising, and stores it with a spatially predictive entropy coder that ships no decoder. Because the anchors are spatially grounded, the binding is predictable and therefore highly compressible. The transmittance-weighted lift and multi-view denoising yield a clean, view-consistent assignment, so the entropy coder spends almost no rate on correcting noise and instead codes only the residual against its spatial prediction. CoSAG reaches sub-megabyte storage while matching or exceeding the state of the art across the 2D-rendered, 3D-selection, and dense-LSeg protocols, reducing field size by 37 to 76x relative to LangSplatV2 at higher accuracy.

Computed tomography (CT) is a critical imaging modality for clinical diagnosis, but reducing radiation dose inevitably introduces severe noise and structured artifacts that degrade image quality. Existing deep learning-based low-dose CT (LDCT) reconstruction methods are typically optimized for fixed dose levels or specific anatomical regions, limiting their robustness and generalization in realistic clinical settings. We propose GenDiff, a generalizable diffusion-based framework for LDCT reconstruction that jointly models continuous radiation dose and anatomical information within a unified reconstruction network. The proposed framework integrates a Dose-Anatomy Encoder to learn acquisition-aware embeddings, a dose- and anatomy-conditioned cold diffusion backbone for iterative refinement, a physics-consistency update to enforce fidelity to the CT forward model, and a Structural Prior Refinement Module (SPRM) that preserves anatomical structures while suppressing dose-dependent artifacts. Extensive experiments on multi-anatomy clinical datasets, including unseen ultra-low-dose conditions as well as out-of-distribution phantom and animal datasets, demonstrate that GenDiff consistently outperforms state-of-the-art convolutional neural network and diffusion-based reconstruction methods. The proposed approach achieves superior reconstruction quality while maintaining strong robustness across different dose levels, anatomical regions, and acquisition domains, making it a promising solution for practical low-dose CT imaging.

Existing optical flow methods broadly follow two paradigms: iterative optimization and diffusion-based estimation. Iterative methods, exemplified by RAFT, achieve high accuracy through recurrent refinement, but remain challenged by large displacements and complex motion. Diffusion-based methods introduce generative modeling and show promise in such ambiguous regions. However, existing diffusion models usually denoise the entire dense flow field from Gaussian noise, including simple regions where reliable motion can already be estimated by a lightweight network. This increases the denoising burden and may cause slow convergence and unstable training. To address this issue, we introduce FlowPainter, a diffusion-based optical flow framework that reformulates dense-flow generation as confidence-guided soft inpainting. FlowPainter employs a lightweight confidence-aware network to predict a rough flow and a pixel-wise confidence mask, distinguishing reliable simple regions from uncertain hard regions. The resulting simple-flow prior is used for confidence-based initialization and further injected into iterative denoising through confidence-gated residual guidance. With dynamically decaying guidance strength, FlowPainter stabilizes early denoising while preserving the flexibility of the diffusion model for late-stage detail refinement. Extensive experiments on public benchmarks, including Sintel, KITTI, and Spring, show that FlowPainter achieves strong accuracy under comparable training settings and converges more efficiently than existing diffusion-based optical flow methods, with notable gains on challenging benchmark splits. Our approach offers a practical way to integrate reliable discriminative priors with diffusion-based refinement for optical flow estimation. Our code is publicly available at https://github.com/mya012/FlowPainter.

Real-world sRGB image denoising remains challenging due to the nonlinear characteristics of sensor noise and the difficulty of acquiring aligned clean-noisy image pairs. Supervised denoisers often overfit to limited paired datasets, while self-supervised methods still depend on sufficiently diverse noisy observations. These limitations motivate scalable noise synthesis methods that can model real-world noise without clean ground truth or camera metadata. We propose YeTI, a real-world sRGB noise generation framework that learns from only two noisy observations of the same scene. YeTI uses a Reconstruction Autoencoder to disentangle scene structure and noise characteristics, and models the latent noise distribution with a one-step Conditional Diffusion Transformer trained using consistency objectives. Given a single noisy input at inference time, YeTI generates realistic, signal-dependent noise while preserving the underlying scene content. Extensive experiments demonstrate the effectiveness of YeTI across real-world benchmarks. We evaluate noise generation on SIDD and further assess generalization on SIDD+, MAI2021, and SID, covering smartphone and diverse consumer-camera sensors. Downstream denoising results on DND further show that denoisers trained with YeTI-synthesized images achieve strong real-world performance, highlighting the practical value of clean-image-free and metadata-free noise generation.

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.

Score matching controls average error under the forward marginals, but a discretized reverse-time sampler evaluates the learned score along its own trajectory. We show that small forward-marginal error does not guarantee numerical stability. We construct a single smooth score field with arbitrarily small forward-marginal $L^2$ error. The learned reverse-time process is nonexplosive, has moments of every order, and can be arbitrarily close to the exact reverse-time process in path-space total variation. Yet its Euler--Maruyama discretizations converge in probability while every positive moment diverges. Thus weak convergence can hold even though every Wasserstein distance $W_p$, $p\ge1$, diverges. The same failure can occur within one fixed finite neural architecture. We construct a family of bounded, globally Lipschitz denoisers for which both the forward-marginal error and the path-space total variation distance tend to zero, while their Euler--Maruyama endpoints diverge in every $W_p$. For compactly supported data, we also give a simple positive result. Projecting the learned denoiser onto a known bounded closed convex set containing the support preserves pointwise accuracy, gives grid-uniform moment bounds, and yields Wasserstein convergence under mild local regularity. Experiments with a small fixed DiT-style network show large growth along rare numerical trajectories and its suppression by denoiser projection, while overall trajectory errors remain small.

Recent advances in 3D Gaussian Splatting (3DGS) have enabled high-quality, render-ready scene representations for novel-view synthesis. However, most existing 3DGS pipelines rely on multi-view observations (or non-causal access to future frames) to achieve sufficient coverage, which is often unavailable in on-device robotics and AR settings where sensing is restricted to a single stereo rig. Recovering a high-quality 3DGS scene from one stereo observation, therefore, remains challenging due to occlusions, limited field of view, and missing geometry. We present StereoSplat+, a diffusion-enhanced feed-forward framework that enables causal reconstruction from a single stereo pair. Our method builds on two key components. First, we propose StereoSplat, an input-invariant feed-forward 3D Gaussian estimator that takes a variable number of posed stereo pairs as input and predicts high-quality 3D Gaussians. StereoSplat fuses complementary geometry cues via a cost-volume branch and a triplane-based 3D volume branch and leverages continuous pose encoding to generalize across view counts and camera configurations. Second, since multiple posed stereo pairs are typically unavailable at inference time, we introduce a diffusion-enhanced one-shot progressive inference scheme called StereoSplat+: starting from one stereo pair, we render novel stereo views from the predicted 3DGS, refine them with a one-step diffusion enhancer, and feed them back as additional inputs to update the 3DGS. Experiments on the KITTI-360 dataset show that StereoSplat+ improves novel-view rendering quality and geometry accuracy, especially in occluded regions and under strong view extrapolation, outperforming recent feed-forward 3DGS baselines.

Human mobility data are essential for transportation optimization, urban planning, and resource allocation, yet real-world mobility data are costly to collect and difficult to share due to privacy concerns. Recent diffusion-based methods have shown promise in synthesizing realistic mobility patterns, but they typically rely on continuous or latent spatio-temporal traces, limiting their ability to natively model discrete semantic events with explicit region, activity, time, and interval structures. To address this issue, we introduce MobiDiff, an end-to-end discrete diffusion framework that efficiently generates mobility data by directly denoising multi-channel semantic skeletons, avoiding the costly interpolation, latent trace construction, and coarse-to-fine realization pipelines widely used in existing diffusion-based methods. Specifically, MobiDiff decomposes each human check-in event into spatial, activity, and temporal channels, and employs structured event-, group-, and channel-level masking to jointly capture trajectory-level mobility patterns and within-event dependencies. We evaluate generation fidelity, privacy-preserving, and efficiency on three large-scale real-world datasets from Atlanta, Boston, and Seattle. Results show that MobiDiff effectively preserves trajectory length and temporal interval distributions while remaining competitive across broader mobility statistics; it is also much faster than state-of-the-art methods, e.g., 5.3$\times$ faster than GeoGen on average during inference. These findings suggest that discrete diffusion offers an interpretable and efficient framework for synthetic mobility data generation.

Forecasting the future anatomy of slow-evolving neurodegenerative diseases could enable earlier, more targeted intervention and improve clinical trial design, but it remains challenging because true progression signals are subtle in longitudinal MRI. In this low-signal regime, transferring modern generative sequence models directly is unreliable: training is dominated by stable baseline anatomy and confounded by dense, sample-specific nuisance variation. We first provide a theoretical analysis that explains these failures through two modes. Identity collapse occurs when optimization is driven toward reproducing the current anatomy, which prevents the model from learning faint temporal change. The continuous interpolation trap arises when standard smooth networks cannot separate localized biological drift from pervasive noise, which leads to spurious changes that diffuse across the volume. To address both issues, we propose Latent Drift, a progressive generative framework that learns change in a compressed semantic representation rather than synthesizing full-resolution anatomy. This design removes pixel-level identity from the prediction target and concentrates model capacity on progression-relevant dynamics. We further apply Finite Scalar Quantization to the learned change representation, which suppresses small, high-frequency nuisance fluctuations while preserving consistent structural drift. Experiments on longitudinal 3D brain MRI show that Latent Drift improves patient-specific neuro-forecasting over diffusion and autoregressive transformer baselines across generative fidelity and clinically relevant evaluation metrics. Project page: \href{https://cutepkq.github.io/latent-drift}{https://cutepkq.github.io/latent-drift}.

Deploying classifier-free guidance (CFG) diffusion models under real-world compute budgets requires quantization, yet existing post-training quantization (PTQ) methods treat CFG models as single-branch networks, ignoring the paired conditional/unconditional structure that CFG inference fundamentally relies on. This structural blind spot has two consequences. At the system level, the two-pass CFG execution pattern imposes a latency overhead that parameter-count and bit-operation metrics conceal entirely, and commodity INT8 inference stacks fail to realize the theoretical efficiency gains that BOPs calculations promise. At the algorithmic level, calibrating against the guidance gap alone admits an exact null space: a quantized model can achieve perfect gap-fidelity diagnostics while the unconditional branch drifts arbitrarily, corrupting every guided prediction at inference time. This paper terms this the branch-drift trap, proves its existence analytically, and confirms it empirically through a false-positive result in which the best-calibrated model by standard diagnostics simultaneously produces the worst sample quality. To close the trap, Guidance-Aware Mixed Precision (GAMP) is proposed, which calibrates directly on the guided prediction, derives per-layer activation-bit sensitivity from guided-output degradation, and allocates bits via a greedy knapsack -- provably preventing unconditional branch drift by construction.

Designing functional and aesthetically coherent floor plans requires exploring a vast space of possible room arrangements, a task that quickly becomes overwhelming for human designers. In this paper, we propose GRE-Diff, a controllable and interactive diffusion-based framework that automates the creation and editing of apartment floor plans under user-specified constraints. By combining AI-generated suggestions with real-time, human-in-the-loop editing, the system enables users to specify room types, room counts, boundary shapes, and editing operations through LLM-parsed instructions or GUI-based interaction. It then generates a diverse set of plausible and well-structured designs for refinement. At the core of our approach is Gaussian Room Embedding (GRE), a continuous latent representation that models each room as a spatial Gaussian distribution capturing its location and extent. Extensive experiments on the RPLAN dataset show that GRE-Diff produces high-quality, constraint-aware, and editable polygonal layouts, offering a practical step toward bridging AI-driven automation and human creativity in spatial design.

How diffusion models circumvent the curse of dimensionality to learn complex distributions over high dimensional spaces from a finite training set, instead of memorizing it, remains a fundamental mystery. To address this, we introduce analytically tractable Bayesian information restricted diffusion (BIRD) models, in which each pixel observes restricted information about noisy data. A BIRD model time-reverses diffusion by inferring which past training sample produced its current restricted observation using the Bayesian posterior. This model class generalizes existing analytical diffusion models that use spatially local information restriction. We show that spatially local BIRD models closely approximate trained diffusion models \textit{early in training}, across different architectures such as UNets and DiTs. Under minimal assumptions on the data distribution, we identify an information-theoretic phase boundary between memorization and generalization in the joint space of amount of training data, time in the reverse generative process, and amount of information restriction: a BIRD model memorizes when the mutual information between its restricted noisy observations and the training data exceeds the log number of training points, and it generalizes otherwise. Experiments across a range of datasets confirm our theoretically predicted location for the transition. We find that generation proceeds near the edge of memorization: both spatially local BIRD models and early-training diffusion models track the memorization-generalization phase boundary by increasingly restricting information over time. Overall, our results reveal a fundamental role for information restriction in generative AI to circumvent the curse of dimensionality.

Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design. Yet, scaling these models to large graphs remains an open problem. We approach this question in the dense-graph setting through the lens of graphons, the size-agnostic limit objects of dense graph sequences, to study how structural graph statistics behave across node-size scales. This perspective leads to DiPhon, a diffusion framework for size-scalable graph generation. Specifically, we formulate a continuous diffusion process on the graphon space via a Jacobi stochastic differential equation (SDE), and propose DiPhon, a discretized graph-level process that mimics these dynamics on finite graphs. We further derive the corresponding reverse-time process, which requires access to the marginal score. For the Jacobi process, this score interestingly admits a tractable form, which we estimate from data via graph denoising and plug into the reverse process to generate graph samples. We prove that DiPhon matches exactly the first moment of the marginal distributions induced by the continuous graphon process, and approximates the second moment up to a closed-form discrepancy. Thus, DiPhon inherits key size-agnostic statistical properties of the graphon dynamics, providing a principled route toward scalable graph generation. Empirically, we demonstrate this scalability by training on small graphs and generating progressively larger graphs at inference time, without retraining, while preserving their core topological properties.

Perceptual quality enhancement of severely compressed videos remains challenging due to complex artifact patterns and substantial information loss. Recent diffusion models have demonstrated strong generative capability for visual restoration, but directly applying them to compressed video often ignores compression degradation characteristics and may introduce structure-inconsistent hallucinations. To address this issue, this paper presents a diffusion-based compressed video enhancement method, named DiffCVE. Coding Prior-enhanced Dual Conditioning (CPDC) branches are designed to jointly model compressed video and coding prior conditions, where coding priors including residuals and motion vectors provide complementary structural and motion guidance during the diffusion denoising process. To make the diffusion process aware of compression severity, a Compression Degradation Semantic Prompting (CDSP) mechanism is introduced to leverage QP-conditioned textual prompts together with LoRA fine-tuning. In addition, a Coding Prior-guided Weighted Fusion (CPWF) module is incorporated into the VAE decoder to fuse VAE encoder and coding prior encoder features with QP-predicted weights. Extensive experiments demonstrate the effectiveness of the proposed method in improving perceptual quality, especially under severe compression settings. The project page with enhanced video demonstrations is available at https://wqmaker.github.io/projects/DiffCVE/.

Quantum diffusion models provide a physics-consistent route to generative learning by formulating noising and denoising directly on quantum states. However, applying such models to classical high-dimensional data is constrained by the qubit cost of state encoding and the computational burden of simulating large density operators. We propose a scalable hybrid generative pipeline that combines a classical autoencoder for dimensionality reduction with a mixed-state quantum denoising diffusion probabilistic model (MSQuDDPM) operating in the learned latent space. The autoencoder compresses data into compact latent codes that can be embedded into a small-qubit Hilbert space, after which the quantum diffusion model learns a generative distribution over latent density operators and decodes samples back to the original domain. Algorithmically, we simplify the reverse dynamics by predicting an estimate of the clean state $ρ_0$ at timestep $t$ and computing the one-step reverse update via an analytic backward propagation rule, rather than learning an explicit predictor for $ρ_{t-1}$. We demonstrate the proposed approach on MNIST image generation and discuss how mixed-state quantum diffusion can serve as a practical backbone for hybrid quantum--classical generative modeling under realistic qubit budgets.

Prior work suggests that diffusion representations capture low-level geometry but struggle with high-level semantics. We demonstrate that state-of-the-art video diffusion models overcome this limitation. By systematically probing their intermediate activations using recent mutual-kNN alignment metrics, we reveal a highly structured latent space where visual representations evolve across both network depth and noise levels. We show that while moderate noise levels yield linearly separable global semantics, fine-grained details persist at lower noise levels but become spatially scattered, requiring attention mechanisms to decode. Building on these insights, we introduce Gen4U (Generation for Understanding), a framework that repurposes these generative representations with a single forward pass. Our experiments establish that frozen, large-scale video diffusion models function as highly competitive video encoders across a wide spectrum of tasks, spanning semantic and non-semantic objectives (video classification, depth estimation, camera pose estimation, image and video captioning). Bypassing fine-tuning, Gen4U unifies the generation and understanding paradigms, achieving strong perception performance while fully preserving the model's ability to generate high-quality video.

Diffusion models offer a powerful framework for sampling from complex probability densities by learning to reverse a noising process. A common approach involves solving for the time-reversed stochastic differential equation (SDE), which requires the score function of the evolving sample distribution. The logarithm of this distribution's density is governed by a Hamilton-Jacobi-Bellman (HJB) type partial differential equation (PDE). However, current methods for solving this PDE, such as PINNs or trajectory-based techniques, often suffer from long training times and significant sensitivity to hyperparameter tuning. In this work, we introduce a novel and efficient solver for the underlying HJB equation based on the functional tensor train (FTT) format. The FTT representation leverages latent low-rank structures to efficiently approximate high-dimensional functions, enabling both model compression and rapid computation. By integrating this efficient representation with a backward-in-time iterative scheme derived from backward stochastic differential equations (BSDEs), we develop a fast, robust and accurate sampling method. Our approach overcomes primary bottlenecks of existing techniques, enabling high-fidelity sampling from challenging target distributions with improved efficiency.

Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs. However, our principled understanding of attention-based graph denoising remains limited, making it unclear whether standard attention is the right mechanism for this task. Here we show that, under a denoising objective, linear attention is suboptimal and can only learn an average spectral denoising filter over the training distribution. This creates a fundamental limitation as graphs often vary spectrally across the distribution. To overcome this limitation, we introduce Spectral Attention, which directly utilizes the input graph spectrum and provably outperforms linear attention by a margin governed by the spectral diversity of the distribution. We then derive Graph Convolutional Attention (GCA), a practical and permutation-equivariant realization of this idea that implements spectral denoising through graph-filtered queries and keys. For stochastic block models, GCA provably matches the idealized Spectral Attention mechanism. We further show that the softmax operation, that follows the attention, provides additional denoising by approximately projecting noisy eigenvectors onto the clean eigenspace. Empirically, replacing linear attention with GCA consistently improves graph denoising and diffusion on synthetic and real datasets, with gains strongly correlated with spectral diversity. In DiGress, GCA matches standard graph-transformer performance without computing expensive structural features, and when combined with the recently proposed PEARL positional encodings, avoids explicit eigendecomposition computations resulting in faster inference without degrading quality. The code can be found here: github.com/shervinkhalafi/graph_conv_att

Image outpainting extends an image beyond its original borders, requiring seamless style integration and globally coherent scene completion. Building on the success of diffusion models, recent methods have achieved substantial improvements in visual quality. In practice, however, high-resolution outpainting is commonly performed via progressive expansion around a fixed source image, particularly in artwork scenarios. Despite this progress, existing approaches still suffer from three key limitations: (i) the absence of a reliable global planning mechanism, which leads to structural instability and error accumulation at high resolutions; (ii) limited spatial controllability beyond text prompts, making it difficult to place objects at user-specified locations; and (iii) high inference latency caused by inherently sequential patch generation. To address these issues, we propose a global blueprint-guided two-stage diffusion framework for layout-controllable high-resolution outpainting with efficient parallel synthesis. In Stage 1, we generate a low-resolution global blueprint using a layout adapter that injects bounding-box conditions into a Stable Diffusion inpainting backbone, producing a globally consistent structural plan while extracting global guidance features. In Stage 2, we synthesize high-resolution local patches in parallel by injecting the blueprint-derived global guidance and initializing each patch from the blueprint using the low-frequency preservation property of forward diffusion. This design eliminates sequential dependency while maintaining global coherence. Extensive experiments on large-scale artwork datasets demonstrate improved visual fidelity, stronger semantic consistency, and substantially reduced inference time compared to prior baselines, while uniquely supporting explicit layout control for artwork outpainting.

Recent diffusion-based generative models have shown impressive performance in image generation and editing. However, due to memory limitations and the high cost of collecting high-resolution training images, existing methods are typically restricted to inputs with linear resolutions below 1K. In contrast, photos captured by modern mobile devices often reach linear resolutions up to 8K, revealing a significant gap between current capabilities and real-world demands. Simply upscaling low-resolution edited results often results in visually enlarged but blurry images that lack fine details. This paper introduces UltraDiffEdit, a novel, tuning-free image editing framework that extends off-the-shelf latent diffusion models (LDMs) to ultrahigh resolutions. UltraDiffEdit employs a multi-scale progressive editing strategy, iteratively blending high-resolution edited content with unedited areas in a coarse-to-fine manner. We employ multi-patch encoding to preserve both edited and unedited visual details within the latent space. To mitigate editing artifacts, our global-local consistency denoising technique consistently integrates edited and unedited latent features, ensuring smooth transition at editing boundaries from the latent representation to the final image. We also introduce a patch-based hybrid sampling approach that captures local, intermediate, and global features, ensuring semantic coherence and enhancing fine detail during denoising. We conduct extensive experiments demonstrating UltraDiffEdit's superior editing quality and flexibility: it can handle image resolutions up to 8K using only a single NVIDIA GeForce RTX 3090 GPU. The source code is publicly available at https://github.com/LonglongaaaGo/UltraDiffEdit.

We propose D2PO (Dynamic Direct Preference Optimization), a principled framework for optimizing diffusion sampling policies with respect to timestep schedules and classifier-free guidance (CFG) weights. Our work is motivated by a fundamental limitation of existing student-teacher regression frameworks; low-NFE student samplers are trained to mimic high-NFEteachers, often sacrificing high-frequency texture fidelity while preserving coarse global structures, thereby misaligning the sampler with perceptual quality. D2PO addresses this challenge by reformulating sampler optimization as a preference-based alignment problem, leveraging the Direct Preference Optimization (DPO) framework. To make DPO applicable to diffusion samplers, we model the sampling policy as an energy-based model (EBM), transforming preference comparisons into tractable energy differences. We further introduce a novel energy formulation derived directly from the pretrained score network, enabling preference evaluation in perturbed spaces that jointly capture structural consistency and fine-grained details. Moreover, we introduce dynamic preferences, where the preferred samples used for alignment progressively improve as the sampling policies are learned. This self-improving mechanism replaces rigid static teacher supervision with an iterative, preference-guided refinement process, providing progressively stronger alignment signals. Extensive experiments demonstrate that D2PO aligns diffusion samplers with perceptual quality more faithfully, unlocking the full potential of high-quality teachers and consistently outperforming conventional regression-based schedulers under low-NFE constraints.

What does a discrete diffusion model learn: a denoiser, a score ratio, or a bridge plug-in predictor? At the level of jump rates, these are one object in different coordinates, and reading a neural network in the wrong coordinate changes the process being trained and sampled. Starting with a rigorous derivation of the continuous-time Markov chain (CTMC) ELBO for any noising process, boundary terms included, we prove the \emph{Oracle Distance} theorem: the negative ELBO is exactly equal to the data entropy plus the path KL from the oracle reverse process to the learned one, not merely a bound. Its unique optimizer is therefore the conditional expectation of the true reverse jump rate given the current noisy state, and its irreducible cost is the rate at which the forward process $Z_t$ destroys information about the clean data $Z_0$, $-\tfrac{d}{dt}I(Z_0; Z_t)$, so every noising process shares the same best achievable negative ELBO: the data entropy. For sequences with token-factorizing noise, the oracle projection yields three exact coordinates for the optimizer: denoiser, cavity (bridge plug-in), and score, with closed-form conversions among them. This framework identifies which law each loss in the literature actually optimizes, recovering MDM, UDM, SEDD, and GIDD as special cases; explains why denoiser and cavity coincide for masked diffusion but not for uniform diffusion; proves that a denoiser parameterization makes the uniform ELBO diverge at initialization while the bridge plug-in stays finite; and calibrates ELBO implementations exactly at initialization. Every identity is verified numerically, without approximation, on an exactly solvable model.

We introduce the first multiplayer world model for highly dynamic environments governed by complex physical interactions. Whereas single-player world models treat the other agents as part of the environment, ours conditions on the action streams of multiple agents, learning to attribute changes in the scene to the correct player and to stay coherent under arbitrary combinations of their actions. We study this problem in the game of Rocket League, where players compete and cooperate under fast, tightly coupled dynamics. Trained on 10,000 hours of gameplay collected with publicly available bots, our 5-billion-parameter latent diffusion model generates four-player matches in real time, producing 20 frames per second on a single Nvidia B200 GPU. Although trained only on short clips, its rollouts stay stable far beyond the training horizon: distributional quality holds steady out to five minutes, the longest horizon we measure, and in practice we observe rollouts continuing for hours with no sign of collapse. We systematically investigate the central design choices: the video codec, the generative objective, and the multiplayer conditioning scheme. In addition, we characterize how behavior changes with model and data scale, including the capabilities that emerge and the failure modes that persist. We further develop targeted evaluations that probe the model's physical understanding rather than visual appearance alone. To support continued research on multiplayer world models, we release our dataset, our full training and inference codebase, and a live demo.

Personalized incentive allocation is vital for e-commerce, where uplift modeling is the standard for estimating Individual Treatment Effects (ITE). However, traditional models often fail in complex multi-seller environments with violations of the Stable Unit Treatment Value Assumption (SUTVA). We identify two critical challenges: Seller-level Cannibalization, where incentives shift expenditure between shops without growing the platform, and Incentive-level Cannibalization, where organic conversions or alternative rewards introduce significant noise into incrementality estimation. In this paper, we propose CanniUplift, a unified framework to mitigate these dual-source cannibalization effects. Specifically, we design Platform-level Global Alignment (PGA) to capture cross-shop substitution through global GMV consistency constraints. To tackle incentive-driven noise, we introduce Redemption-based Decomposition Denoising (RDD), which uses redemption behavior to decompose treated outcomes and reduce attribution noise within an entire-space framework. Furthermore, a Treat-Attention mechanism is designed to model intricate interactions between users' historical behaviors and current treatment options. Extensive experiments on both synthetic and large-scale industrial datasets demonstrate that CanniUplift significantly outperforms state-of-the-art baselines. Ablation studies confirm that the integration of PGA and RDD consistently improves wAUUC and wQINI. Successfully deployed online, our framework achieved a 4.08% relative increase in platform-wide incremental GMV (Delta GMV) over the production baseline and improved ROI in online A/B tests, proving effective in driving global platform growth.

Text-to-image (T2I) diffusion models have achieved striking progress but still struggle to synthesize rare concepts involving unusual attribute-object pairings, often resulting in concept omission or semantic drift where a dominant entity overwhelms the generation. Tracing these failures to a lack of compositional balance during the denoising trajectory, we propose RADIANCE, a training-free framework that treats inference as a closed-loop feedback process. RADIANCE augments pretrained backbones with three modular components: (1) a Compositional Similarity Monitor (CSM) that tracks the emergence of objects and attributes in intermediate latents via CLIP-based feedback; (2) a Bidirectional Scale Controller (BSC) that applies a reactive "restoring force" using positive and negative IP-Adapter scales to rebalance biased trajectories; and (3) a Feedback Guidance Scheduler (FGS) that coordinates these updates across timesteps without additional training. We further extend the framework to multi-object prompts via Delayed Adapter Activation (DAA) and Layer-wise Alternating Guidance (LAG) to prevent premature concept fusion. By overlapping monitoring and denoising through pipelined execution, RADIANCE maintains competitive latency while significantly enhancing the per-sample success rate and effective throughput. Experiments on RareBench and T2I-CompBench demonstrate that RADIANCE consistently enhances compositional alignment and perceptual quality over state-of-the-art baselines.

Reinforcement learning in real world environments often suffers from severe performance degradation due to delayed feedback. Existing approaches typically mitigate performance degradation caused by observation delays by constructing augmented states or predicting the true states. However, these methods often overlook the inherent discrepancy between delayed state and true states induced by stochastic MDP. We theoretically prove the existence of such a discrepancy and show that it leads to the degradation of the optimal policy. To address this challenge, we propose Diffusion Guided Uncertainty Aware Delayed Policy Optimization (DUPO). Our method explicitly models the relationship between delayed state message and the current state using a diffusion model, and leverages the resulting discrepancy estimates to weight delayed policies. Extensive experiments on continuous robotic control tasks with multiple stochastic delays demonstrate that DUPO consistently outperforms existing methods and remains effective even under long and random delay scenarios.

High-resolution velocity models are crucial for reservoir characterization and subsurface delineation. However, the band limited nature of our surface recorded data limits resolution. Utilizing well measurements to enhance the resolution of our subsurface models is an important objective. To this end, we present a diffusion-guided framework for structurally preconditioned velocity-model reconstruction from sparse well-log information. The proposed approach combines plane-wave PDE regularization, structurally preconditioned inversion, and measurement-guided diffusion posterior sampling within a unified formulation. Local structural slopes estimated through plane-wave destruction are used both to propagate well information along geological dip directions and to guide the diffusion sampling process through a joint velocity--slope generative prior. Numerical experiments on the Volve synthetic model and the Viking Graben field dataset demonstrate that the proposed framework improves structural continuity, lateral consistency, and geological realism compared with conventional structurally preconditioned inversion approaches while maintaining computationally practical inference through DDIM sampling.

Sequential Monte Carlo (SMC) methods are a natural tool for post-hoc conditioning of pretrained generative models, but in many applications the mutation kernels used by the particle system are biased approximations of an ideal Feynman--Kac flow. This paper develops a non-asymptotic error analysis for such SMC samplers. Under forward-smoothing forgetting conditions, we decompose the total error into a kernel bias, measuring the effect of replacing the ideal transition kernels by approximate ones, and a finite-particle Monte Carlo error. Our approach relies on extending local Doeblin-type conditions and Lyapunov drift arguments for Markov kernels to conditional distributions, thereby enabling a principled control of the bias. We then instantiate this general framework for conditional sampling with score-based diffusion models, and derive the first non-asymptotic error bound that jointly controls initialization error, time discretization, and score approximation in the reverse diffusion dynamics as well as finite-particle Monte Carlo error.

Text-guided diffusion inversion is central to image editing, where an image is mapped to an initial latent and then edited by replaying the denoising process under a modified prompt. In practice, however, inversion is often performed with a lower classifier-free guidance(CFG) scale than the one used for generation or editing. This mismatch is empirically useful but leaves a basic question unresolved: when a target image is generated by a high-CFG trajectory, when can that trajectory actually be inverted? We study this question in a controlled generation--inversion--reconstruction setting, where the true initial latent and denoising trajectory are known. Using prompts taken from an existing diffusion-editing benchmark, we generate images under high CFG and reconstruct them with fixed-point inversion using the same prompt and guidance setting. The results reveal three types of prompt-level reconstruction behavior: easy prompts that reconstruct for most initial latents, hard prompts that fail for most initial latents, and intermediate prompts whose success depends on the prompt--latent pairing. To analyze the generation side, we define prompt pressure, a step-wise measure of how strongly CFG moves the denoising update away from the unconditional trajectory. Total pressure correlates with reconstruction quality and separates easy from hard prompts, but it does not explain the success or failure of intermediate prompt--latent pairs. Text-side analyses further show that the main visual subject and wording can change inversion difficulty. Finally, we evaluate a compact trajectory-consistency intervention that relaxes guidance only at locally unstable inverse steps. This diagnostic check improves reconstruction and Prompt-to-Prompt editing in our controlled setting, supporting the view that high-CFG inversion failure requires local, trajectory-aware analysis.

While modern video diffusion models excel in visual fidelity, maintaining long-range physical consistency remains a formidable challenge. Conventional pixel-reconstruction objectives mainly focus on appearance details and often fail to capture the underlying dynamics of a scene. To mitigate this, recent efforts have integrated auxiliary modalities (e.g., optical flow) to introduce physics priors via joint training with video appearance. However, these methods have three main limitations: (1) they do not distinguish the different motion patterns of different entity types; (2) joint modeling of visual and auxiliary modalities can cause capacity conflicts and weaken the pretrained visual prior; and (3) auxiliary modalities may accumulate errors during inference. To address these issues, we propose \textbf{VPT}, a fine-tuning framework for improving physical consistency in video diffusion models. VPT introduces a role-aware signal that groups entities into agents, controlled objects, passive objects, and background, so that different physical roles can be modeled more clearly. We further propose a modality-decoupled denoising strategy, where the visual and auxiliary channels are assigned independent noise levels. Together with a loss-weight decay strategy, this design makes auxiliary modalities serve as soft constraints rather than strong dependencies, mitigating recursive prediction errors during inference. We also introduce cross-step auto-guidance to further strengthen physical dynamics. Experiments show that VPT improves physical consistency while preserving visual quality, achieving relative gains of 39.4% in SA and 17.9% in PC on VideoPhy benchmark over Wan2.1-T2V-1.3B, and consistent improvements on VideoPhy-2 benchmark. The project page is available at https://tom-zgt.github.io/VPT.

Inference-time scaling for text-to-image generation has progressed from simple Best-of-$N$ (BoN) sampling to guided search methods that verify and steer candidate trajectories at intermediate denoising steps. These approaches focus on when and how often to verify during denoising but largely treat the cost of generation itself as fixed. Moreover, the standard practice of comparing methods by number of function evaluations (NFEs) counts only denoising forward passes and ignores verifier overhead, which can distort efficiency rankings. We show that under wall-clock evaluation, simple BoN already matches or outperforms several guided search techniques, suggesting that compute is better spent on broader exploration than on repeated intermediate verification. This motivates Flash-BoN, which generates a large pool of inexpensive draft candidates by combining three complementary acceleration knobs: timestep truncation, layer skipping, and activation proxies into a single configuration optimized once per model. An efficient multi-stage verification procedure then identifies the most promising draft, which is refined at full quality. Across three benchmarks and three model scales, Flash-BoN consistently outperforms all baselines under fixed wall-clock budgets, with gains that grow at larger model scales (+8% AUC). We further show that our strategy combines well and improves existing orthogonal techniques such as reflection-based prompt optimization (+16% AUC). The gains correlate with increased candidate diversity, which also enables draft-guided selection to accelerate RL post-training convergence.

Diffusion models (DMs) are a state-of-the-art generative method to approximately sample from an unknown distribution. Their training and evaluation primarily rely on an Evidence Lower Bound (ELBO), which relates the Kullback-Leibler (KL) divergence of model samples to the score matching loss along the path, which serves as a tractable surrogate. The difference between sample quality and the score matching loss produced by this bound leads to the \emph{score matching gap}, which is known to be tight in the worst-case but not descriptive of sample quality in general. In this work, we provide a theoretical analysis of this gap, developing tighter bounds for three metrics: KL divergence, reverse KL divergence, and Wasserstein distance, effectively exploiting the regularity of the class of score estimators. Our results suggest that the quality of the score approximation has more impact on closing the score matching gap for low noise scales. To obtain these bounds, our key technical insight is to exploit the contraction properties of the backward processes. In particular, we rely on entropy flows, logarithmic Sobolev inequalities and reflection couplings, rigorously linking the ergodicity of the Langevin diffusion to the score matching gap problem.

Accurate work-zone geometry perception is critical for intelligent transportation systems, and ultra-wideband sensing offers a low-cost approach for infrastructure-aided reconstruction. However, outdoor UWB ranging is often degraded by non-line-of-sight propagation, burst noise, and long-tail errors, which can distort downstream spatial reconstruction. We present GAIA, a geometry-aware, infrastructure-anchored learning framework that couples temporal range modeling with latent anchor-layout estimation and deterministic distance projection. GAIA preserves range denoising as the supervised task while orienting the learned distances toward boundary-consistent reconstruction. We evaluate GAIA on a real-world outdoor UWB dataset with synchronized UWB, GNSS, and IMU measurements, and further test robustness using a real-data-calibrated stress-test simulator. GAIA achieves the lowest overall range MSE and highest polygon IoU among evaluated filtering-based and learning-based baselines, reducing MSE by 18.4% and improving polygon IoU by 15.5% over PoseMLP. These results show that geometry-aware range denoising provides an effective path toward spatially coherent work-zone reconstruction.

Multi-task offline safe reinforcement learning (RL) promises to learn a shared optimal safe policy from offline data across multiple tasks. This paradigm provides an effective means for the widespread application of RL in multi-task scenarios with high risk and interaction costs. However, the triple challenges of multi-tasking, safety constraints, and out-of-distribution (OOD) actions pose a significant hurdle for existing methods to ensure safety while maximizing reward returns. In this work, we propose a Conditional Diffusion model with Contextual Prompts (CDCP) to address these challenges. Concretely, we first rethink the requirements and challenges in current multi-task decision-making and control scenarios and establish the objectives of multi-task offline safe RL. Subsequently, we transform the multi-task constrained optimization problem into a conditional generation problem using the diffusion model. Based on this, we design a classifier-free guided cost-constraint strategy to provide flexible cost constraints and eliminate extrapolation errors from OOD actions via supervised learning. Additionally, we introduce a novel contextual prompting method to enhance multi-task representation accuracy and adaptability to unseen tasks. A gradient loss synchronization strategy is also introduced to eliminate gradient interference, improving training stability. Finally, extensive experiments demonstrate that the CDCP algorithm exhibits higher performance and safety in multi-task scenarios than the current state-of-the-art baseline methods. It meets different cost constraints without further training, providing a more flexible cost-constraint solution for the multi-task safe RL.

Diffusion models have become a dominant paradigm for conditional image generation, yet existing approaches generally follow two directions: task-specific designs that can improve performance but limit generalization, and training-free loss guidance that compresses rich conditions into scalar objectives and applies stepwise guidance, leading to information bottlenecks and error accumulation along the sampling trajectory. Given the urgent need for an effective unified framework across diverse conditional image generation tasks, we propose Data Injection and Contrastive Trajectory Refinement (DICT), a training-free inference method that enhances conditional image generation without introducing task-dependent architectures. DICT introduces Data Injection, where noise-perturbed conditional signals are integrated into early denoising stages; by performing guided denoising on these injected signals, DICT adaptively selects and distills task-salient information from the raw condition, effectively preserving spatial richness and ensuring precise condition-to-generation alignment. Furthermore, DICT applies Contrastive Trajectory Refinement across adjacent denoising states, enabling pairwise comparisons that progressively improve sample quality. These designs keep inference simple while improving cross-task transfer under a unified diffusion formulation. Extensive experiments on conditional image generation tasks (e.g., style transfer, image super-resolution, and image deblurring) show consistent gains in fidelity and perceptual quality over representative task-specific and loss-guided baselines.

Diffusion models have recently been repurposed for zero-shot classification, giving rise to diffusion classifiers that identify the best-matching text prompt by minimizing the noise-prediction error. Despite their growing adoption, how these models make classification decisions remains poorly understood. We introduce ASOB-Bench, a bias evaluation for diffusion classifiers along three dimensions: Attribute binding, Size-Order bias, and Background dependency. These dimensions serve not as an exhaustive taxonomy but as targeted probes of how the text-conditioned reconstruction-error score reaches a decision. Such a perspective is well studied for discriminative vision-language models, yet remains overlooked for diffusion classifiers. Extending an existing framework with five new attribute categories on newly constructed datasets, we find diffusion classifiers are less prone to attribute misbinding than an OpenCLIP baseline; on the established ComCo benchmark they are substantially more susceptible to size-order shortcuts; and on ImageNet-B they suffer far larger accuracy drops, revealing heavy reliance on background over foreground cues. Reconstruction-error heatmaps and U-Net cross-attention visualizations expose the mechanism behind each bias. Because diffusion classifiers share the same denoiser as text-to-image models, these single-pass diagnostics also point toward analogous failure modes in generation. Overall, diffusion classifiers exhibit a distinct bias profile from vision-language models, offering guidance for building more robust diffusion-based models.

Prior studies have demonstrated that diffusion classifiers achieve robust zero-shot classification performance. However, their effectiveness is strongly tied to the pretraining data distribution: they perform well in majority, high-density regions of the data manifold, but are significantly less accurate in minority, low-density regions. Although prior works on minority sampling have focused on generating more minority-like images, what minority sampling fundamentally enables beyond generation remains underexplored. In this paper, we reveal a direct relationship between minority sampling in generation and the perception capability of diffusion classifiers. Specifically, we show that enhancing minority sampling broadens the coverage of underrepresented regions on the data manifold, thereby improving diffusion-based recognition. To exploit this connection, we propose \textit{Self-Improving Diffusion Classifiers with Minority Preference Optimization} (MiPO), which fine-tunes a pretrained diffusion model using minority preference rewards. Using only arbitrary caption data, MiPO generates candidate samples, rewards those that better cover minority regions, and optimizes the model with LoRA and Group Relative Policy Optimization, without additional image data, external foundation models, or external reward models. This enables stable, prompt-adaptive minority sampling and translates low-density generative coverage into improved zero-shot diffusion classification. To sum up, we show that diffusion classifier perception is biased toward majority regions, demonstrate that this bias can be alleviated through minority preference optimization, and evaluate MiPO on five standard datasets.

Classical training-free denoisers such as BM3D and non-local means owe much of their strength to search: content-dependent block matching whose memory traffic and data-dependent control flow parallelize poorly and preclude fixed-latency implementations. Learned denoisers reach the highest quality, but they need training data, degrade outside their training domain (which we also observe), and carry per-pixel compute budgets that effectively require a GPU. We present GALOSH (Generalized Anscombe LOcal SHrinkage), a redesign of training-free denoising that removes the search entirely and aims at multi-domain coverage, speed, and quality at once: a blind per-image Poisson-Gaussian noise fit, a generalized Anscombe transform, a two-pass local Walsh-Hadamard shrinkage of luminance, and a luminance-guided local regression of chrominance -- two deliberately different operators for the two perceptually different noise components, each with its own strength control. Every stage is local, data-independent, and regular -- the same computation graph for every pixel of every image. One core serves two domains: raw Bayer mosaics and sRGB/YUV images. On four real-noise benchmarks (SIDD Medium and RawNIND, raw and sRGB) GALOSH is consistently the strongest among the tested blind, training-free methods -- surpassing BM3D- and NLM-family baselines even when those are given an oracle noise level -- and approaches trained networks on raw data while remaining below in-domain trained networks at high ISO in sRGB. Being search-free makes it fast: 7x-650x faster than the DL baselines on the same GPU at full benchmark size, and the only strong method in the comparison that also runs practically on plain CPUs. The fixed, data-independent structure is designed to map naturally onto fixed-point and streaming hardware, supported by an operation-count analysis and a working INT16 fixed-point realization.

Few-step distilled diffusion students cut text-to-image inference from ~50 to 1-8 network evaluations, but the quality gap is usually summarised by a single FID/CLIP scalar that cannot say which axis of the conditioning response changed, nor whether a behaviour comes from the architecture, the distillation objective, or simply from being a diffusion model. We replace the scalar with a decomposable probe that injects controlled perturbations along three layers (prompt encoder, denoiser input, denoiser output) under three modes (mean, variance, scale) and six strengths, reporting a bootstrap-median Bures W2^2 selectivity ratio on Inception features. Under a single matched estimator across 23 models -- five teachers and 18 distilled students spanning five backbone families (SDXL, SD1.5, SD3.5, PixArt-alpha, FLUX), three architecture classes (UNet, DiT, MMDiT), and five distillation paradigms -- the three layers read three empirically separable factors: the prompt layer is a universal prompt-mean response (a sanity channel, not a discriminator), the latent layer reads the prediction type, and the score layer reads the distillation objective. Our main result: within this sweep, the latent layer is a near-binary detector of rectified-flow backbones. Its ratio exceeds 1 across a sustained low-to-mid band only for rectified-flow models (SD3.5, FLUX); no epsilon-prediction model qualifies. A matched epsilon-prediction control (PixArt-alpha) rules out wide-T5 conditioning, and the fingerprint survives adversarial (ADD) distillation as both teacher and student. Two secondary score-layer findings hold under narrower scopes: a canonical 4-step ADD-vs-rest contrast on the UNet families with a non-ADD baseline, and a CI-separated trajectory-rollout early-strength score spike on both UNet and DiT. All ratios are CI-citable under one estimator; we release the per-cell tables and the estimator.

Decentralised federated learning, based on peer-to-peer communication, is increasingly proposed for on-device training of machine learning models, promising a privacy-preserving, communication-efficient training process with no risk of single-point failure. However, the role of structural and temporal inhomogeneities in such fully decentralised settings remains poorly understood. Here, we investigate their effects when model parameters are locally averaged during aggregation. We show that the decentralised federated learning process is governed, both in the early phase and the late, stationary limit, by the same dynamics as a lazy random-walk diffusion process on temporal networks. Based on this mapping, we demonstrate that the typical experimental scenario used in decentralised federated learning leads to unrealistically rapid convergence because of ignoring the temporal and structural inhomogeneities inherent in the communication network. We analyse real-world temporal networks and find that inhomogeneities most often dramatically slow down diffusion, hence the convergence process.

Controllable generative models of 3D medical images can synthesize volumes with specified clinical attributes, but this demands samples that are simultaneously high-fidelity, natively 3D, and faithful to the requested conditioning. We present CONFLUX, a latent diffusion model for chest computed tomography (CT): a 3D variational autoencoder compresses each volume, and a rectified-flow transformer generates in the latent space. Generation is conditioned on structured radiological metadata (18 abnormality findings, sex, age, and reconstruction kernel) through adaptive layer normalization. The model leads strong volumetric baselines on tri-planar Frechet distance (FID 32.3 vs. 74.6 for MAISI) while exposing direct control over clinical attributes. To strengthen that control we add an online reinforcement-learning post-training stage (group-relative policy optimization) that rewards how reliably a classifier recovers the requested findings from each generated volume. Judged by a separate, independent classifier, post-training removes 47% of the shortfall relative to real-scan reliability. We release the model and a ~200k synthetic chest-CT dataset with conditioning metadata spanning a wide variety of clinical findings.

Single-image reflection removal (SIRR) aims to recover the clean transmission layer from a reflection-contaminated image. Although recent methods achieve promising results with large diffusion models, they rely on image-agnostic adaptation strategies, e.g., fine-tuning or ControlNet, that enforce uniform suppression regardless of reflection severity. As a result, heavy reflections often leave residuals, while weak ones suffer from detail loss. To this end, we propose ReLo-IRR, a reflection-guided LoRA framework built upon the rectified flow model. First, a lightweight estimator is designed to predict the reflection strength descriptor, providing an explicit prior of reflection dominance for each image and enabling image-dependent LoRA modulation. Second, we introduce a time-conditioned mechanism that fuses this reflection descriptor with timestep embeddings, enabling LoRA modulation to evolve consistently with the coarse-to-fine denoising process. By jointly modeling reflection strength and denoising dynamics, our ReLo-IRR achieves robust suppression of diverse reflection conditions. Extensive experiments on challenging benchmarks validate the effectiveness of ReLo-IRR, demonstrating superior dereflection performance and robust generalization. The code is released at https://github.com/KONGBAI-8080/ReLo-IRR.

Convolutional Neural Networks (CNNs) achieve strong denoising performance by exploiting spatial context from neighboring pixels. Deep Image Prior (DIP) leverages this property to restore images from a single noisy input without requiring large datasets. However, the over-parameterized architecture of DIP often leads to noise fitting during optimization. In this paper, we propose Pool-DIP, a convolution-free architecture that incorporates pooling-based contrast modeling to capture spatial context efficiently. Pool-DIP improves denoising performance while significantly reducing the number of parameters and computational complexity compared to convolution-based DIP models. Experimental results show that Pool-DIP achieves competitive performance across multiple datasets, including a real-world benchmark. Spectral analysis further reveals that Pool-DIP stabilizes the evolution of high-frequency components during optimization and suppresses erroneous high-frequency signals. The proposed architecture also generalizes well to other image restoration tasks such as super-resolution and inpainting.

Molecular optimization often starts from a pretrained generative model that captures a broad prior over valid molecular structures. At test time, however, the goal is not to sample from this prior, but to use a limited oracle budget to shift generation toward task-specific high-reward molecules. We study this adaptation problem for discrete diffusion models. Each online round couples several choices. The loop must decide which candidates to evaluate, how rewards become model updates, which feedback to reuse, and how far to move beyond the pretrained prior. These choices have mostly been studied in isolation, leaving open whether they complement one another, become redundant, or interfere inside a full online adaptation loop. We conduct controlled studies across six small-molecule binding-affinity tasks and three protein-fitness tasks. We find that acquisition, reward shaping, and model debiasing provide complementary routes to higher reward, especially for small molecules. Replay further stabilizes learning, while validity penalties keep small-molecule exploration on the valid molecular manifold. Together, these findings point to a practical recipe for feedback-efficient molecular optimization: online fine-tuning with acquisition, reward shaping, debiasing, replay, and validity control. This recipe outperforms offline fine-tuning and inference-time search baselines under matched oracle-call budgets and GPU-hour accounting. The gains are largest when high-reward candidates require larger shifts from the pretrained prior.

High-throughput long-context generation is one of the central challenges for large language models. Generation is typically memory-bandwidth-bound rather than compute-bound: each decoding step must stream the accumulated key/value (KV) cache from memory, so bandwidth demand grows with context length while only one token is emitted. Two parallel approaches have therefore emerged: reducing memory access with efficient attention variants and linear-time mixers such as Mamba, or increasing parallel computation by generating blocks of tokens at once. However, technical challenges arise when combining these two ideas. Earlier hybrid diffusion models such as DiffuMamba use bidirectional Mamba mixing, including a reverse-direction scan relative to causal generation. This reverse scan needs to scan the entire sequence, so its states are not prefix-only and cannot be precisely reused as a cache even when diffusion is performed block by block. We propose a BDLM Mamba--attention hybrid that addresses this challenge by restricting the reverse Mamba scan to the active denoising block, which enables exact caching across blocks. In an 87M-parameter DCLM sweep, BDLM Mamba-H achieves the best C4-en validation perplexity compared to BDLM attention and full-sequence baselines. At 350M parameters, it remains competitive with BDLM attention. For long-context inference, BDLM Mamba-H reaches 19.7x the throughput of full-sequence DiffuMamba-H at 65K tokens and 3.7x the throughput of BDLM attention at 262K, showing that Mamba hybrids are a potential long-context diffusion architecture.

Benign overfitting and double descent have come to shape our understanding of generalization in deep learning, establishing that overfitting is not only compatible with good generalization but can actively benefit it. Diffusion models share much of the machinery of standard deep learning, so it is natural to assume that they also exhibit these properties. In this work, we show that this assumption is largely incorrect. We first establish fundamental impossibility results showing that, unless the sample size grows exponentially with the data dimension, overfitting and good generalization cannot occur simultaneously. Consequently, the population loss follows a classical U-shaped curve in model complexity rather than exhibiting double descent. Analyzing a simplified setting, we identify a key difference between regression and score matching: regression benefits from an alignment between the target and the empirical covariance; score matching admits no such alignment, leaving overfitting irreparably harmful. We further identify implicit regularization stemming from time-smoothness of the score and early stopping during training as mechanisms that prevent such overfitting and verify our findings with high-dimensional image generation experiments. Our results reveal that generalization in diffusion models is governed by mechanisms distinct from those of traditional regression, motivating the development of new theory.

While diffusion models have revolutionized image synthesis, their application to real-world inverse problems is often hampered by the need for massive datasets and the difficulty of imposing strict physical constraints. In this work, we introduce \textbf{SE-UNet} (Singular Equivariant UNet), a framework designed to solve ill-posed imaging tasks without extensive pre-training. By treating generation as an optimization problem constrained by geometric equivariance ($D_4$ group) and singular value gating, SE-UNet effectively standardizes the solution space. We demonstrate that these strong inductive biases allow for state-of-the-art zero-shot inpainting results (80% missing pixels) on CIFAR-10. Our method surpasses Deep Image Prior (DIP) baselines by over 4 dB in PSNR and exhibits a characteristic "singular snap" convergence -- rapidly locking into the signal manifold. SE-UNet thus offers a data-efficient pathway for constrained generation, aligning with the ReALM-GEN goal of bridging theoretical priors with practical deployment.

We study timestep allocation for score-based diffusion sampling, where a learned reverse-time dynamics is discretized on a finite grid. Uniform and hand-crafted schedules are standard choices, but they rely on fixed prescriptions and can therefore be suboptimal. To address this limitation, we propose Adaptive Reparameterized Time (ART), a continuous-time control formulation that learns a time change by treating the speed of the sampling clock as the control, so that a uniform grid on the learned clock induces adaptive timesteps in the original diffusion time. Based on a leading-order Euler error surrogate, ART provides a principled objective for allocating timesteps along the sampling trajectory. To solve this deterministic control problem, we introduce ART-RL, an auxiliary randomized formulation with Gaussian policies that turns schedule learning into a continuous-time reinforcement learning problem. We prove that the randomized ART-RL formulation is equivalent to ART at the optimizer level, in the sense that its optimal Gaussian policy recovers the optimal ART time-warping rate through its mean. We further establish policy evaluation and policy improvement characterizations and derive trajectory-based moment identities that yield implementable actor--critic updates for learning the schedule. Across experiments ranging from controlled low-dimensional settings to image generation, ART-RL can be plugged into existing diffusion samplers by changing only the timestep grid, consistently improving sample quality over strong baseline schedules at matched budgets while leaving the rest of the sampling pipeline unchanged. The learned schedules also exhibit broad generalization, transferring without retraining across sampling budgets, datasets, solvers, pipelines, and representation spaces.

The rise of customized diffusion models has fueled a boom in personalized visual content creation, but it also introduces serious risks of malicious misuse, thereby posing threats to personal privacy. Image aesthetics are strongly correlated with human perception of image quality. Motivated by this observation, we address facial privacy protection from a novel aesthetic perspective by degrading the generation quality of maliciously customized models, thus reducing facial identity leakage. Specifically, we propose a Hierarchical Anti-Aesthetics (HAA) framework that exploits aesthetic cues at multiple perceptual levels. HAA consists of two key branches: (1) Global Anti-Aesthetics, which degrades overall aesthetics and generation quality by constructing a global anti-aesthetic reward mechanism and a corresponding loss; and (2) Local Anti-Aesthetics, which disrupts facial identity by using a local anti-aesthetic reward mechanism and loss to guide adversarial perturbations toward facial regions. By integrating both branches, HAA achieves anti-aesthetic degradation from a global to a local level during customized generation. Extensive experiments show that HAA outperforms existing methods in identity removal, providing an effective tool for protecting facial privacy.

Discrete diffusion models have steadily improved in quality relative to autoregressive (AR) models. However, these models are normally constrained to fixed-length generation and do not support key-value (KV) caching. Block diffusion partially bridges diffusion and AR by generating token blocks left-to-right, but its fixed-size sequential blocks limit decoding flexibility and parallelism. Here, we present a new class of language models, set diffusion, comprised of (i) a likelihood parameterization that factorizes over flexible-position, flexible-length token sets and (ii) a set-causal diffusion architecture that supports KV cache updates after every inference step. By factorizing over token sets instead of fixed-size blocks, tokens can be decoded in arbitrarily-ordered sets, including sliding-window sets, enabling faster inference and support for any-order decoding. Set diffusion achieves better speed-quality tradeoffs on mathematical reasoning, summarization, and unconditional generation compared to prior diffusion language models while offering stronger infilling performance than block diffusion. We provide the code, along with the model weights and blog post on the project page: https://m-arriola.com/setdlms/

Text driven hand object interaction (HOI) generation is gaining attention for immersive applications and robotics, yet producing physically plausible interactions remains challenging. Even when individual motions appear natural, small contact errors can cause conspicuous artifacts such as floating and interpenetration. Prior methods mitigate these issues using explicit contact cues or implicit grasp priors, but typically rely on multi stage pipelines and fail to model temporally evolving contact. We present JointHOI, a single stage diffusion framework that jointly generates 3D hand object motion and dynamic, distance based contact maps from text. By treating contact as an auxiliary inner modality, joint generation enables the model to learn contact motion coupling during training. At inference, contact guided sampling enforces consistency between generated contact maps and motion implied geometry, improving temporal stability and reducing penetration and floating. Experiments on GRAB and ARCTIC demonstrate consistent improvements in text adherence and physical plausibility over prior methods.

These notes give a proof-oriented introduction to diffusion models from the viewpoint of sampling, tracing a single arc from classical sampling dynamics to modern diffusion samplers, their error analysis, and inference-time control. Throughout, the material is layered into core definitions and identities proved in full, representative estimates proved under simplifying assumptions, and research-level theorems stated with a proof roadmap. The intended audience is beginning graduate students with a background in probability but no prior exposure to stochastic differential equations, stochastic numerics, or diffusion models.

We investigate volumetric reconstruction for compressive sensing light-sheet microscopy (CS-LSM), where fast volumetric imaging is achieved by encoding multiple axial planes into each camera exposure. To recover the underlying volume from highly multiplexed measurements, we propose a plug-and-play (PnP) framework that flexibly incorporates any user-specified denoiser into the reconstruction process. Building on a slice-based formulation, we further introduce an axial-coupled model that exploits correlations between adjacent slices to improve volumetric continuity. For efficient computation, we derive a Woodbury-based update for the data-consistency step in both the slice-based and axial-coupled formulations, and employ a Gauss-Seidel sweep for the denoising step in the axial-coupled model. Under a weakly convex regularization assumption, we establish subsequential convergence of the proposed algorithm. Experiments on synthetic and real zebrafish-heart data demonstrate that the proposed framework successfully recovers cellular structures from compressed measurements, and provide practical insights into the comparative performance of commonly used denoisers within the PnP framework under the CS-LSM setup.

High definition map generation is essential for autonomous driving, yet remains a labor-intensive process at scale. We present MapDreamer, a generative diffusion model that synthesizes lane-level vector maps with explicit topology directly from a single aerial image. MapDreamer learns a compact latent representation of lane centerlines and their topological relations using a variational autoencoder and predicts graphs with a transformer-based latent diffusion model. To align generated maps with the observed scene, we condition each denoising step on dense aerial features injected through cross-attention. To handle the varying number of lanes across scenes, we propose a lane cardinality module paired with background ghost lane latents, a learned buffer that prevents slot collapse during diffusion. Furthermore, we introduce a sliding-window global graph aggregation strategy that stitches local tiles into city-scale maps while preserving connectivity through encoded lane boundaries. Experiments on UrbanLaneGraph derived from Argoverse 2 show improved geometric and topological fidelity over non-generative baselines.

We present SynLaD, a latent diffusion framework for small-molecule generation that unifies ligand-based drug design objectives (what to make) with synthetic accessibility (how to make it). Current models typically optimize one objective at the expense of the other, creating a bottleneck for discovering high-scoring and synthesizable molecules. SynLaD combines reaction-constrained generation with pharmacophore-conditioned 3D design by learning a latent space that decodes to both 3D structures and synthesis pathways. An encoder maps molecules to a latent representation used by two decoder heads: (i) a geometric head that reconstructs atom types and coordinates and (ii) an autoregressive synthesis head that outputs synthetic routes in a serialized, reaction-based notation. A diffusion transformer generates novel latents in the learned space, conditioned on pharmacophore profiles. Across analogue generation tasks for bioactive ligands, SynLaD outperforms existing baselines in synthesizable and diverse hit generation, demonstrating that a single model can produce shape-aligned molecules with feasible synthesis plans.