Discrete Diffusion Model

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

Discrete diffusion models are widely used for learning and generating discrete distributions. As the generation process is inherently sequential, the acceleration of sampling is of significant importance. In this work, we parallelize the mainstream $τ$-leaping algorithm for absorbing discrete diffusion in a Continuous-Time Markov Chain (CTMC) framework. By leveraging the continuous-time stochastic integral form of the $τ$-leaping algorithm and the Picard iteration method, we achieve parallel-in-time sampling acceleration and provide a proof of exponential-factorial convergence for our algorithm. We improve the overall time complexity of $τ$-leaping under absorbing settings from ${\mathcal{O}}(d \log S)$ to ${\mathcal{O}}(\log (d\log S)\cdot \log d)$ with respect to NFE. Empirically, our method shows consistent acceleration across synthetic and real-data settings. The new sampler achieves at most $7$--$9\times$ runtime speedup for synthetic distribution, and maintains the same quality with $50\%$ fewer NFE and $1.45$--$1.86\times$ runtime speedups in image/text tasks on a single GPU. Our research expands the potential of discrete diffusion models for efficient parallel inference, with broader implications for applications such as molecular structure and language generation.

Modern one-step diffusion models achieve impressive quality through distribution-based timestep distillation. Yet, they rely on a critical assumption: Teacher and Student must inhabit the same latent space. This Shared-Space constraint prevents knowledge transfer from modern high-capacity Teachers (e.g., SD 3.5 and Flux) into compact, deployment-friendly Students such as SD 1.5, whose latent resolution and VAE parameterization differ from the Teacher. We formalize this overlooked regime as Cross-Space Distillation, where Teacher and Student differ in both latent resolution and VAE space. To enable distillation under this mismatch, we introduce the Bridge, a lightweight latent interface that maps Student latents into the Teacher space without modifying the Student backbone. Bridge combines a frozen Student VAE decoder as a spatial prior with a compact learnable projector, and is trained with latent reconstruction and attention fidelity objectives for stable Teacher-space alignment. Across diverse modern Teachers, Bridge enables substantial gains for compact one-step Students; for example, it improves SD 1.5 from 5.4 to 9.4 HPSv3 while preserving one-step inference, low latency, and broad ecosystem compatibility. These results show that heterogeneous large Teachers can be distilled into efficient, deployable backbones through a lightweight latent-space interface.

Reconstructing physics-based 3D assets -- geometry, materials, and illumination -- from multi-view images is a core problem in computer graphics and vision, and a prerequisite for realistic relighting and editing. Physics-based inverse rendering offers an accurate image-formation model, but is severely underconstrained: without strong priors, illumination is baked into materials, and reconstructions generalize poorly to novel views and lighting. Data-driven diffusion models, in contrast, predict visually plausible materials, yet their predictions rarely satisfy the rendering equation and are not directly usable for physics-based rendering. We bridge these two paradigms rather than replacing either. Our key idea is to treat the predictions of a state-of-the-art diffusion model not as target material values but as a similarity kernel for optimization: we introduce a regularization loss that penalizes deviations in the optimized material over surface regions where the diffusion predictions are near-constant, while leaving the optimization free to match the input images. Built on this regularizer, our end-to-end pipeline jointly reconstructs geometry, materials, and illumination, yielding high-quality assets that drop into standard rendering pipelines and relight faithfully. On the Synthetic4Relight, Stanford-ORB, and DTC-Synthetic datasets, our method significantly outperforms state-of-the-art baselines in both reconstruction accuracy and relighting quality.

We consider sparse multivariate stochastic systems that evolve in continuous time according to a causal mechanism and present methodology to recover the system's time-infinitesimal transition mechanism from mere cross-sectional data. This observational paradigm is motivated by applications such as gene expression analysis, where destructive experimental techniques may only allow recording data once over a cell's lifetime. Precisely, we assume the system follows a time-homogeneous diffusion process that has reached an equilibrium distribution at observation time. Further, we assume the causal mechanism is fully described by the diffusion drift, is acyclic, and its causal structure graph is known. In this setting, we prove that the full causal mechanism, i.e., the drift function, can be non-parametrically identified under a weak non-explosion criterion. We derive a non-parametric kernel estimator for this challenging inverse problem and prove its consistency. Moreover, we propose a cross-validation scheme for hyperparameter tuning, illustrate the behavior of our estimator in simulations, and we discuss connections with irreversible generative diffusion models and low-frequency sampled data.

Recent progress in Text-to-Image generation benefits from large-scale Text-Image pairs. However, the scarcity of Text-LiDAR pairs often causes over-smoothed scenes and limited controllability. In this paper, we rethink the limitations of Text-LiDAR generation task, focusing on alleviating insufficient training priors and constructing controllable Text-LiDAR data. We propose a \textbf{T}ext-\textbf{to}-\textbf{L}iDAR \textbf{D}iffusion \textbf{M}odel for LiDAR scene generation, T2LDM++, with a Self-Conditioned Representation Guidance (SCRG). Specifically, to alleviate object over-smoothing, SCRG employs a Guidance Network (GN) to provide reconstruction-based soft supervision to the Denoising Network (DN). This enables DN to learn geometry-aware representations through reconstruction guidance, leading to more accurate denoising in DDPMs. Meanwhile, through analysis and design, SCRG exhibits more effective and lightweight, while decoupled in inference, avoiding computational overhead. Furthermore, we construct two high-quality Text-LiDAR benchmarks ($>$100K samples) using a generalized strategy of geometric annotations, along with a controllability metric. Moreover, a directional position prior is designed to mitigate street distortion, further improving scene fidelity. Additionally, T2LDM++ supports multiple conditions, including (Semantic, Box, BEV, Camera)-to-LiDAR, Sparse-to-Dense, and Dense-to-Sparse generation, by learning a control encoder via frozen DN. With effective prior modeling and high-quality Text-LiDAR benchmarks, T2LDM++ can generate realistic LiDAR scenes with rich geometric details in unconditional and conditional settings.

Image-based Virtual Try-On (IVTON) has greatly advanced through diffusion models, yet existing methods require many sampling steps and depend on masks with costly auxiliary networks. In addition, the absence of large-scale mask-free paired datasets further limits the development of mask-free IVTON. We propose FDM-MFVT, a few-step diffusion model for mask-free IVTON, integrating an Outfit-aware Noise Optimization Module (OANO) and an Instruction-driven Try-on Module (IDT) to enhance efficiency and flexibility.The OANO module initializes the alignment space with noise using the input image and only needs 6 steps to generate a higher-fidelity try-on image compared to 30 steps.The IDT module uses virtual try-on prompts and efficient adaptation to generate high-quality results from garment and person images alone. We further introduce MFVT, a 30,000-pair mask-free IVTON dataset. Experiments show that FDM-MFVT achieves superior quantitative and qualitative results with fewer inference steps than mask-based and mask-free baseline methods.

Real-world object removal is challenging due to two key difficulties: the target object's non-local effects, such as shadows and reflections, which are difficult to model, and the fact that user-provided masks are often inaccurate or incomplete. With billions of parameters and tens of denoising steps, diffusion-based models achieve strong removal performance at the expense of substantial computational cost, limiting their use in interactive applications and on edge devices. To address these challenges, we present OSOR (One-Step Object Removal), which simultaneously achieves efficient, effect-aware, and mask-robust object removal. Concretely, OSOR introduces: (1) an occupancy-guided discriminator for precise boundary supervision, enabling stable single-step diffusion training; (2) an alpha head that leverages knowledge from pretrained diffusion models to predict appropriate removal regions with minimal overhead, thereby handling imperfect masks; and (3) a semantic-anchored verification pipeline (SAVP) that filters noisy instruction-based triplets to produce effect-aware supervision at scale. Using SAVP, we curate CORNE, which contains 280K verified removal pairs, and further annotate AnimeEraseBench and TextEraseBench to evaluate performance on more complex removal tasks. Experiments show that OSOR surpasses strong multi-step diffusion baselines in perceptual quality while achieving $4\times$ to $30\times$ faster inference.

Warm-started diffusion samplers accelerate iterative inference, but it is rarely clear which part of the pipeline carries the gain. We study \textbf{retrieval-warmed energy-based reasoning (RW-EBR)} -- an IRED energy-based diffusion model \cite{du2024ired} augmented with a Modern Hopfield trajectory memory -- and contribute a \textbf{five-arm ablation methodology} (oracle, best-constant, per-query-random, shuffled, aligned) that separates three confounded effects: class-prior bias shift, stochastic warm-starting, and graph-aligned value reuse. The diagnostic decomposition is adapted from LLM-RAG evaluation \cite{ru2024ragchecker}. On \textbf{connectivity-2} (Erdős--Rényi all-pairs reachability), the aligned-vs-shuffled-oracle swing reaches \textbf{$+35$,pp} balanced accuracy on a fixed 1{,}000-graph validation-set diagnostic, with value distribution and retrieval mechanics fixed, only per-graph alignment destroyed, while per-query random initialisation falls below cold -- per-graph alignment, not bias shift or stochasticity, dominates. Yet the \emph{deployable} cold-prediction pipeline misses the acceptance gate at stored-value quality. The same diagnostic logic, stopped at the key-quality screen, applied to \textbf{Sudoku} with a task-specific key encoder produces a clean negative at a \emph{different} component -- key quality, under the current setup. The decomposition names the first blocking component on each task. The setting -- graph reachability refined by an iterative diffusion sampler, with explainability of failure modes as the lens -- places the work within structured and spatio-temporal reasoning.

The task of compositional generation involves using a conditional generative model, trained only on a subset of the possible conditions, to produce samples from compositionally-defined target distributions such as a geometric combination of the source distributions. In this work, we argue that this task is often infeasible for vanilla conditional diffusion models: we conjecture that no inference-time technique can efficiently produce samples from the target distribution in certain well-motivated settings. This idea is supported by theory-guided generalization arguments and carefully-designed experiments on both synthetic and realistic data. In particular, while recent methods such as Feynman-Kac correction reduce inference-time approximation error, our results show that score estimation error has a more catastrophic effect on performance when the target distribution is out-of-distribution with respect to the sources, highlighting the need for a different approach to this task.

Distilling conditional diffusion models aims to transfer the behavior of a large teacher to a smaller student while preserving alignment across conditioning inputs. Unlike recognition tasks, knowledge distillation in conditional diffusion often struggles to transfer knowledge beyond the training distribution, since the predicted noise strongly depends on the conditioning signal. As a result, effective distillation requires exploring a large conditioning space. In practical settings, this creates a major bottleneck. Paired image-condition data may be limited, and generating synthetic images for every available condition is often computationally infeasible, while the pool of conditions, such as text prompts, can be extremely large. Recent work addresses this issue by switching conditions during training, exposing the student to a broader conditioning space without changing the distillation objective. Yet this raises a complementary question: once a large conditioning corpus is available, how should the training effort be allocated? In this work, we introduce ARIA, a framework that adaptively allocates training effort across coarse regions of the conditioning space. By maintaining online estimates of teacher-student discrepancy at the region level, ARIA focuses updates where misalignment persists while preserving the original distillation objective. Empirically, ARIA improves over RC across most architectures and settings, with the clearest gains observed in unseen and underrepresented regimes. We also provide a theoretical analysis showing that the proposed tracking mechanism follows the evolving discrepancy during training under bounded variance and drift assumptions.

Reference-based diffusion models enable highly controllable image generation by leveraging elements from input images to guide prompt-driven synthesis. However, these models are computationally expensive in runtime, and their cost scales severely with the number of input references. While the efficiency of diffusion models has been extensively studied in the context of prompt-driven generation, it remains largely under-explored in the realm of reference-based models. This setting presents unique challenges not addressed by methods focusing solely on generation. In particular, the wasteful representation of references as dense token grids offers significant opportunities for improvement. In this work, we present Sparse Context, a method for constructing sparse reference representations by retaining only a reduced subset of reference tokens. We observe that even without modifying the model, dropping a significant portion of reference tokens at inference time largely preserves its generation capabilities. To fully realize this potential, we fine-tune the model with random token dropping at varying ratios, encouraging robustness to partial reference representations. Crucially, this training strategy decouples the model from any specific token selection rule, allowing flexible control at inference time. At inference time, instead of random dropping, we apply task-aware token selection strategies that prioritize the most informative regions of the reference images, adapting the token budget to the input and task requirements. Extensive experiments show our method achieves a 4x increase in inference speed for multi-reference generation and an 2x for single reference generation. Importantly, this efficiency is achieved without compromising visual quality across both spatially-aligned editing and subject-driven generation.

Video diffusion models have enabled remarkable progress in video generation and editing. However, content preservation remains a core challenge: existing methods regenerate every pixel and often alter elements that should remain unchanged, such as characters or background scenes. We introduce Vera, a layered diffusion framework for content-preserving video editing. Instead of regenerating the entire video, Vera generates an edit layer along with an alpha matte for compositing with the source video, separating creative editing from content preservation by design. To encourage coherent composition with the source video, we extend the text-to-video DiT into a Mixture-of-Transformers (MoT) architecture, with separate DiTs for each layer that interact through joint self-attention. To support the training of Vera, we further construct a high-quality layered dataset with accurate alpha mattes, diverse scenes and dynamics, and visual effects. Across our quantitative benchmark and human preference study, Vera outperforms leading open-source video editing models in content preservation while remaining competitive in edit quality, using 486K frames of layered training data.

Time series forecasting is a fundamental machine learning task. Recent work has explored Large Language Models (LLMs) for this purpose due to their strong generalization, pattern recognition, and zero-shot or few-shot capabilities. Despite their suitability for long-context learning, LLMs face challenges in multimodal settings: they lack calibrated probabilistic modeling for non-text data and struggle to align heterogeneous representations. To address these issues, we propose a new framework Diffusion-LLM that integrates a conditional diffusion model into an LLM-based forecasting pipeline. This joint design enables learning the conditional distribution of future data while improving semantic alignment in a shared latent space. We evaluate Diffusion-LLM on six long-term forecasting benchmarks, including ETT, Weather, and ECL. Our method consistently outperforms existing LLM-based baseline, achieving notable gains in ultra-long-term and few-shot forecasting and demonstrating the value of distribution-aware regularization for enhancing robustness and generalization in time series LLMs.

Training image generation foundation models consumes substantial resources. Previous methods have attempted to leverage semantic guidance to accelerate the training process, yet their experiments were only conducted on simple datasets such as ImageNet, at low resolutions, and with small-scale models. In this paper, we propose SeFi-Image, a text-to-image foundation model built upon semantic-first diffusion, a novel latent diffusion modeling paradigm. We instantiate SeFi-Image at three model scales, 1B, 2B, and 5B parameters, enabling systematic study of scaling behavior and flexible deployment under varying compute budgets. Notably, our largest 5B model was trained with merely 125K A800 GPU hours, corresponding to roughly 10-20% of the training compute used by Z-Image. However, it achieves results comparable to or even superior to Qwen-Image and Z-Image. Despite this modest training compute, SeFi-Image achieves strong performance on a wide range of benchmarks, including GenEval, DPG, LongTextBench, OneIG, and CVTG-2K. Moreover, we provide DMD2-distilled few-step turbo variants for each model scale to accommodate diverse hardware constraints and latency requirements. We publicly release our code, weights and hope this work offers the community useful insights into semantic-guided diffusion modeling for T2I generation, while also providing practical and readily deployable model options.

We show that replacing the standard MSE denoising loss in diffusion models with a nonlinear transformation induced by an f-divergence yields a simple robust training surrogate that empirically improves performance under data contamination, with small additional computational overhead. The theoretical foundation rests on a local divergence construction: under the Gaussian reverse-kernel structure of DDPM, each per-step likelihood ratio follows a lognormal distribution parameterized by a scalar mismatch, so the conditional f-divergence at each step reduces to a one-dimensional function of the denoising error. Summing these local divergences yields a training objective that unifies diffusion training as divergence induced weighted denoising, where the derivative of the induced divergence acts as a residual-space influence weight that controls the contribution of each sample. Bounded-influence divergences (Hellinger, negative exponential) suppress large error samples, with Hellinger yielding an explicit exponential weight, connecting the framework to robust M-estimation. Empirically, on CIFAR-10 under 30% contamination, NED reduces FID from 93.0 (KL) to 77.5, while also outperforming standard robust losses such as Huber and clipped MSE.

Diffusion models are typically sampled independently, even when the downstream objective is to obtain a diverse set of candidates. We introduce a variance-weighted batch distribution that favours collections of samples with large empirical spread after a prescribed linear feature map. The target is specified explicitly, and the sampler is derived as the corresponding Doob $h$-transform of independent diffusion dynamics. The resulting correction has a compact form: an interaction term that repels posterior denoised means, together with a curvature term that moves particles to the region of higher feature variance. This yields an interacting-particle sampler with a transparent probabilistic target rather than a heuristic repulsive drift.

Standard tokenwise diffusion LMs keep training corruption and inference commitment at token granularity throughout denoising. At high noise, this leaves scattered local fragments rather than coherent evidence, making it hard to form early coarse structure, exactly what planning-sensitive generation requires. Hierarchical planning methods add coarse stages to separate planning from wording, but they need extra planners, block latents, or two stage designs. We propose Noise Dependent Granularity Control (NDGC), a single-level diffusion method that uses the noise level as a granularity cue. NDGC aligns training exposure and inference commitment with denoising progress. High noise steps use coherent token groups to support early meaning commitment, while low noise steps return to token level refinement. This creates planning like coarse to fine denoising without an explicit planner or hierarchical architecture. Across controlled tests, ablations, and WritingPrompts, NDGC shows earlier skeleton formation, better ordered recovery, and healthier outputs.

To generate natural and accurate sentence-level sign language, synthesizing the "gloss", the fundamental semantic unit, is essential. However, most current sign-language production (SLP) methods generate entire sequences at once. While this end-to-end approach is often efficient, it is prone to temporal drift and hand motion blur as sentences get longer, and fails to accurately control individual glosses. In this paper, we propose the Context-aware Gloss-wise AutoRegressive Diffusion model (GARD), a gloss-wise diffusion framework that models coarticulation by conditioning on both semantic (linguistic) and kinematic (motion) contexts. To ensure natural continuity between gloss motions, GARD introduces two additional strategies: i) Inter-Gloss Transition Guidance, which applies gradient-based guidance to kinematically align inter-gloss boundaries and ensure seamless pose consistency. ii) Global Motion Harmonizer, refining the entire gloss motion sequence based on the boundary poses adjusted by Inter-Gloss Transition Guidance. Extensive experiments on Phoenix-T and CSL-Daily datasets demonstrate that GARD achieves superior performance over existing SLP methods in terms of both linguistic accuracy and motion similarity.

Block diffusion language models accelerate decoding through parallel block-wise denoising, yet whether they can be reliably scaled for long chain-of-thought (CoT) reasoning remains unresolved. To this end, we develop DreamReasoner-8B, an open-source block diffusion reasoning model, and conduct a systematic study of how training and inference block sizes affect long-CoT reasoning. Our analysis reveals a stark performance disparity: training with large block sizes yields remarkably poor reasoning, whereas small block sizes preserve effective reasoning. To bridge this granularity gap, we propose block-size curriculum learning, which gradually transitions training from fine-grained to coarse-grained block sizes, thereby overcoming this limitation and enabling strong reasoning performance that generalizes across diverse inference block sizes. On mathematical and code reasoning benchmarks, DreamReasoner-8B achieves results competitive with leading open autoregressive models such as Qwen3-8B. This work establishes a practical foundation for efficient, reasoning-capable diffusion language models. We release our model at https://github.com/DreamLM/DreamReasoner.

Recent advances in generative machine learning models have significantly improved medical imaging, offering promising solutions for data augmentation, privacy preservation, and improved model generalization. However, synthesizing high-quality structural MRI data for Alzheimer's Disease (AD) remains challenging due to the subtle, region-specific, and progressive anatomical changes associated with neurodegeneration. In this paper, we extend the Med-DDPM conditional diffusion model -- originally designed for brain tumor synthesis -- to generate 3D structural MRIs specifically tailored to AD. We adopted Med-DDPM due to its established stability and structural fidelity compared to other generative models, which makes it particularly suitable for capturing the subtle anatomical changes characteristic of AD. Our approach conditions the diffusion process on anatomical segmentation masks derived from the ADNI dataset, incorporating key AD-relevant brain structures into the generation process. We systematically evaluate the quality and utility of the synthetic images by training segmentation models on real, synthetic, and hybrid (mixed) datasets. Experimental results demonstrate that segmentation models trained exclusively on synthetic data achieve comparable Dice scores (0.6532) to those trained on real data (0.6513), while exhibiting significantly enhanced recall. Notably, models trained on hybrid datasets (mixing real and synthetic images) outperform both real and synthetic-only baselines, achieving a Dice score of 0.7244. These findings underscore the successful use of conditional diffusion models for generating anatomically accurate, AD-specific synthetic MRIs, and highlight their potential for enhancing training data availability, improving diagnostic accuracy, and promoting research reproducibility in neuroimaging studies.

Masked diffusion models (MDMs) have recently emerged as a promising paradigm for sequence generation. Scaling MDMs is conventionally achieved by increasing the parameter count or the number of denoising steps. We introduce Recursive Masked Diffusion Models (R-MDMs), which add recursive depth as a third scaling axis by repeatedly applying the same denoising transformer within each diffusion step. Recursion enables iterative refinement of the output through parameter reuse, increasing effective model depth without increasing parameter count. Across structured generation tasks, including Sudoku and Countdown, we show that R-MDMs achieve substantially improved parameter efficiency: a model with $L$ recursive iterations often matches the performance of non-recursive baselines with roughly $L\times$ more parameters. Moreover, recursive refinement can partially substitute for additional denoising steps, allowing recursive models to reach the same generation quality with fewer forward passes at inference time. These results suggest that recursive depth is a practically useful scaling mechanism for MDMs, improving both parameter efficiency and the allocation of test-time compute.

Visual textures -- spatially homogeneous image regions containing repeated elements (e.g. a field of grass, the bark of a tree) -- are ubiquitous in visual scenes and provide important cues for recognizing and analyzing materials and objects. A number of existing texture models extract essential statistics from a single texture image, and can then generate high-quality samples that are visually similar to the original by matching these statistics. However, their statistics are either hand-designed or based on a network pretrained for another purpose (e.g., object recognition). Here, we develop the first principled method for unsupervised learning of a set of statistics that are used to constrain a maximum entropy probability model. We leverage methods developed for generative diffusion models to derive training and sampling procedures, and compare these to the traditional method of sampling via matching the statistics. Despite the compactness of our trained model (512 statistics), it generates texture images whose quality is as good as or better than the current state-of-the-art model (~177k statistics). A more direct comparison of the two models, obtained by synthesizing images that are indistinguishable for one model but maximally different for the other, reveals their relative strengths and weaknesses. Finally, we show that unlike previous statistical texture models, a straight trajectory in the representation space of our model generates homogeneous texture samples that interpolate smoothly between the features of the two end points.

This paper develops constrained diffusion models with primal-dual inference (PDI) to sample from optimal distributions of entropy-regularized optimization problems with \emph{average} constraints. We formalize constrained sampling in the Lagrangian dual domain, where the optimal distribution takes the form of a Gibbs distribution indexed by the optimal dual variable. Rather than estimating this dual multiplier before sampling and freezing it throughout generation, PDI jointly infers the optimal primal distribution and its parametrizing dual variable. Each reverse diffusion step denoises using the score field associated with the current multiplier and then updates the multiplier through dual ascent using the estimated constraint violation of the denoised samples. To enable this conditional score field, we train a single dual-conditioned score network over the family of Gibbs distributions induced by the dual variables encountered during inference. We prove that the time average of the dual variables generated along the inference trajectory converges to a neighborhood of the dual optimum and bound the effect of residual dual mismatch on the terminal distribution through schedule-dependent stability factors. We evaluate PDI on constrained sampling from a mixture of Gaussians, wireless resource allocation, and portfolio management.

Shared-space transportation operation requires low-speed autonomous platforms to navigate safely and efficiently among pedestrians, service robots, micromobility users, carts, and other road users. Most existing systems decompose this problem into trajectory prediction followed by motion planning, which creates one-way information flow: predicted participant futures influence the robot plan, but the selected robot plan cannot influence the predicted multi-agent evolution. This paper presents a joint prediction-planning diffusion framework that treats participant prediction and robot planning as a single conditional trajectory generation problem, where the model samples the future robot trajectory and all participant trajectories from one coupled distribution using a causal Transformer with cross-trajectory attention. To replace heuristic repulsive post-processing, the framework introduces differentiable safety potential guidance, a time-varying occupancy-probability potential whose gradient directly guides the joint sampler, and conditional flow matching is used to reduce inference steps while preserving multimodal trajectory diversity. The evaluation emphasizes shared-space operational effects, including near misses, blockage time, induced participant deviation, hard-braking events, and embedded latency, rather than treating average displacement error and final displacement error as the main result. Experiments in scenario-grounded simulation, naturalistic pedestrian replay, Isaac Sim validation, and ROS/Orin deployment show that joint sampling improves tail safety and runtime efficiency over a separated prediction-then-planning baseline.

RL-based post-training has been widely adopted to enable interleaved visual and textual reasoning in unified multimodal models capable of both text and image generation. However, most existing approaches are built upon autoregressive (AR) unified models, which require full image regeneration during visual reasoning. In this work, we demonstrate that multimodal discrete diffusion models are effective alternatives to AR models for reinforcement learning in interleaved reasoning, owing to their ability to perform efficient visual rollouts via localized visual editing rather than full image-token regeneration. This reduces rollout computation during GRPO by 26.9% compared to AR baselines, with minimal performance drop. Despite the improved efficiency, we find that joint reward assignment, which employs a shared reward signal across modalities, introduces cross-modal interference between unrelated image and text token sequences during RL updates. To address this issue, we propose factorized reward assignment, a strategy that assigns rewards independently to text and vision segments. With factorized reward assignment, our RL approach achieves an 11.2% improvement over joint reward assignment and a 38.04% improvement over the base model.

Learning the compositional nature of the physical world requires joint observation of interacting factors. However, because practical data is often decentralized, these factors are fragmented across isolated silos. Existing decentralized generative approaches focus only on modeling the union of siloed data, overlooking novel combinations implied by the collective whole. To bridge this gap, we introduce Decentralized Compositional Flow Matching (DCFM), a framework that enforces structural constraints across the global set of generative factors, without exchanging any raw data. DCFM enables novel combinations to emerge through peer interactions, even when no single data source can independently support the composition. Empirically, DCFM substantially outperforms federated learning and mixture-of-experts baselines across conditional image generation, robotic spatial planning, and medical attribute co-occurrence modeling.

The abundance of pre-trained diffusion models provides an opportunity for composition. Combining several models, however, runs the risk of one model dominating or models disagreeing with each other. Here, we propose Divide-and-Denoise, a method for coordinating multiple pre-trained diffusion models during sampling. Much like managing a specialized workforce, our method creates a fair but efficient division of labor across models. Central to our method is the notion of an allocation which defines the responsibility of each model to every region of the noisy sample. At every timestep, we then denoise by (i) updating the allocation by solving a fair division game, where we divide the sample into regions that maximize total utility under fairness constraints, and (ii) aligning the models with this allocation, where we guide each model to denoise within its assigned region. This leads to a new composite denoising process that evolves in tandem with a division process. We evaluate Divide-and-Denoise on conditional image generation. Across several quality metrics, including the GenEval benchmark, our method outperforms baselines and resolves common failures including missing objects and mismatched attributes. Experiments show that Divide-and-Denoise utilizes each model's expertise without neglecting any other model.

Diffusion models have advanced 3D shape generation, yet most methods still denoise in high-cardinality spaces (e.g., voxel/SDF grids, meshes, or point clouds), which is computationally and memory intensive and makes it difficult to scale in terms of both higher resolution and stronger controllability. We rethink the diffusion representation and propose to move diffusion from dense geometry to compact geometric primitives, representing each shape as a small set of superquadrics. Instead of operating on thousands to millions of geometric representation values, we leverage 7KB superquadric parameters (pose, size, and shape), drastically reducing diffusion-state dimensionality and per-step compute/memory. Our diffusion-over-superquadrics improves scalability by supporting broader capabilities (e.g., resolution-free point-cloud decoding, part-level editing, and constraint-based design) and achieving competitive surface-fidelity and distributional performance on standard benchmarks after point-cloud decoding, while enabling efficient generation within 0.6s per shape for most conditions.

Bayesian optimization (BO) is a widely used approach for black-box optimization that uses a Gaussian process (GP) as a surrogate and guides sequential evaluations via an acquisition function, with the ultimate goal of locating the global optimum $\mathbf{x}^{\star}$. To align with this goal, information-based acquisition functions such as Predictive Entropy Search (PES) model $\mathbf{x}^{\star}$ as a random variable and reduce the entropy of its distribution, but approximating this distribution via traditional GP posterior sampling is computationally expensive. To address this limitation, we leverage Conditional Diffusion Models (CDMs) to efficiently approximate the distribution of $\mathbf{x}^{\star}$ and develop BO-inherent training strategies for CDMs. Motivated by the structural properties of the CDM-learned distribution, we further develop an acquisition strategy termed Diffusion-based Mode Seeking (DMS) to guide the sequential evaluation. We establish a sub-optimality guarantee for the CDM-learned distribution and demonstrate through extensive experiments that DMS outperforms standard BO baselines.

Score-based generative models have had remarkable success over the last decade in generating a diverse set of visually plausible images. A variety of architectures including CNNs, U-Nets, and Transformers have been used as the score-approximation network in such diffusion modeling; however, to date, relatively little is known about how these architectural choices impact generative behavior. In this work, to provide insight into this area, we propose an analytically solvable parameterization of the score function using an expansion in a 2D orthogonal wavelet basis. In particular, we derive interpretable optimal score functions in terms of the moments of the data distribution. We use this parametrization to provide an architecture-agnostic, moment-based analysis that reveals which attributes of the data distribution tend to matter most for denoising. Our score machine is flexible enough to partially mimic the relevant inductive biases of multiple architectures, including U-Nets, and CNNs, taking a step towards understanding why different score architectures can exhibit distinct generative behavior. Since our score is solvable in terms of the moments of the data, we can begin to understand how the data distribution interacts with the score network to produce the behavior we observe in diffusion models.

Many important outcomes unfold as dynamic cascades, including product adoption, disease spread, financial distress, and information diffusion. A central challenge is to recover the hidden influence network behind these cascades. Existing methods typically assume a specific diffusion model, and their performance degrades substantially when that assumption is misspecified. We propose CascadeNet, a Jacobian-based machine learning framework for network recovery that does not require specifying a diffusion mechanism. The key idea is that the underlying influence structure can be characterized by the Jacobian of the one-step transition function. CascadeNet first constructs a flexible estimator of the transition function, and further applies Neyman-orthogonal debiasing via the Riesz representer, so that the debiased Jacobian is $\sqrt{n}$-consistent and asymptotically normal, enabling formal inference on the network structure. We validate CascadeNet in both a simulation exercise and a real-world empirical application. In simulations, where the data-generating process is known, CascadeNet achieves the highest network recovery accuracy across nine common data-generating processes. In an empirical application to COVID-19 transmission across Spain's 52 provinces, CascadeNet recovers transmission networks that are significantly correlated with the true inter-province mobility network, whereas networks recovered by baseline methods show no significant alignment with the ground truth.

Standard diffusion models corrupt an entire sample with a single shared noise level, forcing all spatial regions to follow the same denoising trajectory. We introduce AsyncPatch Diffusion, a joint-diffusion framework that assigns distinct noise levels to different input dimensions, such as image pixels, or latent tokens. We show how this asynchronous corruption defines a valid generative process while supporting a richer family of spatially heterogeneous denoising trajectories, and prove the first valid ELBO for this process. We show that a single pretrained model can perform spatially adaptive generation, where different regions are denoised on different schedules. A key challenge is training: naive independent noise-level sampling overemphasizes highly heterogeneous configurations and underrepresents homogeneous noise levels, that are crucial during sampling. We address this with a controlled noise-level sampler that regulates both the average corruption level and its spatial variability. AsyncPatch achieves generation quality comparable to conventional diffusion on ImageNet 256 and LSUN, while being natively suited for inpainting without task-specific fine-tuning. We further introduce input guidance, which uses clean or partially corrupted regions to guide the generation of unknown regions, improving local consistency and texture matching. Finally, we demonstrate adaptive generation strategies including uncertainty-guided acceleration and autoregressive sampling.

Standard continuous-time generative models rely on monolithic architectures that must navigate vastly different signal regimes, from isotropic noise to intricate data distributions. While scaling model capacity improves performance, deploying a massive network uniformly across the entire generative timeline is inherently inefficient. In this work, we propose Complexity-Balanced Splitting (CBS), a principled framework for temporal capacity allocation that distributes the generative workload across multiple specialized sub-networks. Grounded in function approximation theory and de Boor's equidistribution principle, CBS partitions the diffusion timeline into segments of equal approximation burden, allocating more representational capacity to regions where the generative dynamics are more difficult to model. To estimate this local complexity, we introduce two complementary and tractable monitor functions: a spatial measure based on the flow's Dirichlet energy, and a geometric measure based on the acceleration of the sampling trajectories. Using a lightweight auxiliary model to estimate these complexity profiles, our approach eliminates the need for heuristic temporal splits or computationally expensive search procedures. Extensive evaluation across multiple architectures (SiT, JiT, and UNet) and datasets demonstrates that CBS consistently improves synthesis quality without increasing per-step inference cost. In particular, CBS improves FID by ~35% on SiT-XL with CFG relative to naive temporal partitioning. Project page is available at https://noamissachar.github.io/CBS/.

Controllable generation with discrete diffusion models is often hindered by high computational overhead or the need for retraining. In this paper, we present \underline{\textbf{G}}radient-\underline{\textbf{I}}nformed \underline{\textbf{L}}ogit \underline{\textbf{C}}orrection (\textbf{GILC}), a plug-and-play framework that efficiently estimates guidance signals by repurposing the pretrained denoising network as a variational proxy. To circumvent the gradient instability inherent in high-dimensional discrete spaces, we introduce a Jacobian-free mechanism that directly corrects the clean prediction logits, facilitating stable and effective guidance. Our method accommodates both differentiable and non-differentiable reward functions. Extensive experiments across DNA, protein sequence, and molecular generation tasks demonstrate that GILC achieves state-of-the-art performance without additional training, frequently outperforming fine-tuning approaches.

Generating realistic synthetic sequential data is critical in real-world applications across operations research, finance, healthcare, energy systems, and scientific computing, where time-indexed observations are used for prediction, simulation, risk assessment, and data-driven decision-making. While diffusion models have achieved remarkable success in generating static data, their direct extensions to sequential settings often fail to capture temporal dependence and information structure. Designing diffusion models that can simulate sequential data in an adapted manner, and hence without anticipation of future information, therefore remains an open challenge. In this work, we propose a sequential forward-backward diffusion framework for adapted time series generation. Our approach progressively injects and removes noise along the sequence, conditioning on the previously generated history to ensure adaptiveness. A novel score-matching objective is introduced for efficient parallel training. We derive rigorous statistical guarantees under a generic framework, then establish score approximation, score estimation, and distribution estimation results with ReLU networks serving as a concrete instance. Empirically, we validate our method on synthetic data, including ARMA models and Gaussian processes, and demonstrate its effectiveness in constructing mean-variance optimal portfolios.

Scenario generation is a critical component in stochastic programming (SP), as it directly influences the quality of decision-making under uncertainty. Existing approaches predominantly rely on either sampling-based techniques or supervised learning using neural networks. Sampling-based techniques often struggle to capture complex dependencies and rare but plausible events, while supervised learning requires fixed input-output pairs for training and is limited in its ability to generate a wide variety of realistic scenarios that are not restricted by predefined patterns or rules. To address these limitations, we introduce Diff2SP, a diffusion-based generative framework that incorporates downstream optimization objectives directly into scenario generation. Unlike conventional methods that treat scenario generation and decision-making as separate steps, Diff2SP embeds stochastic optimization into the training process, enabling the generation of scenarios that are both statistically coherent and decision-aware. To formally justify this optimization-aware design, we establish a regret bounds that link distributional accuracy to decision quality, and establish sample complexity guarantees showing faster convergence than traditional generative models such as GANs. Empirical results on both synthetic and power-system datasets validate these theoretical insights, demonstrating that Diff2SP consistently improves both statistical fidelity and downstream optimization outcomes.

Custom diffusion models (CDMs) have garnered significant interest owing to their remarkable capacity for generating personalized concepts. However, the majority of CDMs unrealistically presume that the user's collection of personalized concepts is static and incapable of incremental growth over time. Furthermore, they exhibit significant catastrophic forgetting and concept neglect of previously learned concepts when incrementally learning a sequence of new ones. To resolve the above challenges, we develop a novel Continually Customizable Diffusion Model (CCDM), enabling users to perform concept-incremental versatile customization. Specifically, we design an attribute-decoupled LoRA (AD-LoRA) module and a relevance-guided AD-LoRA aggregation strategy to mitigate catastrophic forgetting. They can preserve concept-specific attributes of each task and leverage beneficial inter-task correlations to enhance the continual learning of new customization tasks. Additionally, to address the challenge of concept neglect, we propose a controllable regional context synthesis strategy that performs multi-concept composition in alignment with user-provided conditions. This strategy enhances the overall consistency in multi-concept synthesis by guaranteeing semantic independence between user-defined regions and their smooth boundary transitions. Experiments show our CCDM exhibits significant improvements over baseline methods.

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

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

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

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