Discrete Diffusion Model

Diffusion models have achieved remarkable success, yet their training remains inefficient due to a severe optimization bottleneck, which we term Representation Degradation. As noise levels increase, the outputs of the trained model exhibit progressive structural distortion, which can destabilize training and impair generation quality. Our analysis suggests that this instability is driven by mismatched target recoverability, which is associated with Neural Tangent Kernel (NTK) spectral weakening and effective low-rank behavior. To address this, we propose Elucidated Representation Diffusion (ERD), a plug-and-play framework that dynamically reallocates optimization effort according to effective recoverability. By stabilizing representation learning without external supervision, ERD accelerates convergence and achieves strong empirical performance across diffusion backbones.

Trajectories are nowadays valuable information for a wide range of applications. However they are also inherently sensitive, as they contain highly personal information about individuals. Facing this challenge, synthesizing mobility trajectories has emerged as a promising solution to leverage mobility information while preserving privacy. State-of-the-art models, often rely on the false assumptions of generative models implicit privacy and fails to provide privacy guarantees while preserving trajectories utility. Here, we introduce diffGHOST, a conditional diffusion model based on latent space segmentation, designed to answer this challenge. Thus, this paper propose a methodology that identify and mitigate memorization of critical samples using condition segments of a learn latent space.

Recently, diffusion models have attracted considerable attention for magnetic resonance image reconstruction due to their high sample quality. However, most existing methods rely on large networks with opaque time-conditioning mechanisms, and require offline coil sensitivity estimation. This results in limited interpretability of the reconstruction process and reduced flexibility in the acquisition setup. To address these limitations, we jointly reconstruct the image and the coil sensitivities by combining the parameter-efficient product-of-Gaussian-mixture diffusion model as an image prior with a classical smoothness prior on the coil sensitivities. The proposed method is fast and robust to both contrast and anatomical distribution shifts as well as changing k-space trajectories. Finally, we propose a more expressive parameterization of the image prior which improves results in denoising and magnetic resonance image reconstruction.

Discrete diffusion models generate structured sequences by progressively unmasking tokens, but enforcing global property constraints during generation remains an open challenge. We propose primal-dual guided decoding, an inference-time method that formulates constrained generation as a KL-regularised optimisation problem and solves it online via adaptive Lagrangian multipliers. At each denoising step, the method modifies token logits through an additive, constraint-dependent bias, with multipliers updated by mirror descent based on constraint violation. The bias arises as the optimal KL-regularised projection of the constraint, so the constrained distribution remains as close as possible to the model's unconstrained distribution while still satisfying the constraint. The method requires no retraining and no additional model evaluations beyond standard sampling, supports multiple simultaneous constraints, and provides formal bounds on constraint violation. We evaluate our approach on topical text generation, molecular design, and music playlist generation, showing that a single algorithm instantiated via domain-specific scoring functions improves constraint satisfaction while preserving relevant domain-specific quality metrics.

Recent conditional image generation methods can improve controllability by generating images that are faithful to conditions such as sketches, human poses, segmentation maps, and depth. By applying these techniques to image augmentation while preserving annotations, generated images can be used as additional training data and can improve recognition performance. However, for high-level driving tasks such as traffic-rule extraction and driving-behavior understanding, simply using annotations as conditions is insufficient. Instead, images must be augmented while preserving the detailed high-level structure of the original scene. One possible solution is to use multiple conditions so that generated images retain diverse structural cues after generation. However, when multiple conditions are used, conflicts among conditions can prevent reliable structure preservation. In this work, we input semantic segmentation, depth, and edges extracted from the original image into a multi-condition image generation model, thereby providing rich structural information as conditions. We further propose a modeling approach for handling conflicts among multiple conditions and show that it enables image generation with stronger structural preservation. We also build a generation framework and evaluation protocol for driving tasks, establishing a basis for comparison with prior and future models. As a result, this work contributes to image generation research by addressing condition conflicts in multi-condition generation and provides an important step toward mitigating data scarcity in high-level autonomous-driving tasks.

Scene graphs (SGs) represent objects and their relationships as structured graphs, enabling applications in image generation, robotics, and 3D understanding. Recent work suggests that conditioning image generation on scene graphs improves compositional fidelity compared to text-only prompting. However, since users typically provide text rather than structured graphs, a key challenge is to generate scene graphs from natural language. Prior work on discrete diffusion has demonstrated success in generating generic graphs such as molecules and circuits, but fails to account for the hierarchical structure and strong dependencies between objects, edges, and relations in scene graphs. We address this limitation by introducing a dependency-aware, hierarchically constrained discrete diffusion model for scene graph generation. Our approach decouples structure and semantics across the forward and reverse processes, enabling the model to capture conditional dependencies. At inference time, we perform training-free conditioning to sample text-aligned scene graphs. We evaluate our method on standard SG benchmarks and demonstrate improvements over both continuous and discrete graph generation baselines across graph and layout metrics. When fed to downstream image generation, our approach yields improved compositional alignment compared to text-to-image models, particularly in multi-object scenarios.

Existing mobile devices are constrained by compact optical designs, such as small apertures, which make it difficult to produce natural, optically realistic bokeh effects. Although recent learning-based methods have shown promising results, they still struggle with photos captured under high digital zoom levels, which often suffer from reduced resolution and loss of fine details. A naive solution is to enhance image quality before applying bokeh rendering, yet this two-stage pipeline reduces efficiency and introduces unnecessary error accumulation. To overcome these limitations, we propose MagicBokeh, a unified diffusion-based framework designed for high-quality and efficient bokeh rendering. Through an alternative training strategy and a focus-aware masked attention mechanism, our method jointly optimizes bokeh rendering and super-resolution, substantially improving both controllability and visual fidelity. Furthermore, we introduce degradation-aware depth module to enable more accurate depth estimation from low-quality inputs. Experimental results demonstrate that MagicBokeh efficiently produces photorealistic bokeh effects, particularly on real-world low-resolution images, paving the way for future advancements in bokeh rendering. Our code and models are available at https://github.com/vivoCameraResearch/MagicBokeh.

Distilled diffusion models accelerate image generation by reducing the number of denoising steps, but often suffer from degraded image quality. To mitigate this trade-off, test-time optimization methods improve quality, yet their iterative nature incurs substantial computational overhead and leads to slow inference, limiting practical usability. Recent hypernetwork-based approaches amortize this process during training, but still require costly noise modulation in high-dimensional latent spaces. In this work, we propose LENS (Low-frequency Eigen Noise Shaping), an efficient noise modulation framework that operates in a low-dimensional subspace. Our approach is motivated by the observation that low-frequency components of the noise largely determine the global structure and visual fidelity of generated images. Based on this observation, we provide a theoretical justification for restricting modulation to the low-frequency subspace and derive a principled training objective. Building on this, LENS employs a lightweight, standalone network to selectively modulate these components, enabling efficient and targeted noise modulation. Extensive experiments demonstrate that LENS achieves competitive image quality while reducing FLOPs by 400-700$\times$, model parameters by 25-75$\times$, and inference-time overhead by 10-20$\times$ compared to prior methods.

Step distillation has become a leading technique for accelerating diffusion models, among which Distribution Matching Distillation (DMD) and Consistency Distillation are two representative paradigms. While consistency methods enforce self-consistency along the full PF-ODE trajectory to steer it toward the clean data manifold, vanilla DMD relies on sparse supervision at a few predefined discrete timesteps. This restricted discrete-time formulation and mode-seeking nature of the reverse KL divergence tends to exhibit visual artifacts and over-smoothed outputs, often necessitating complex auxiliary modules -- such as GANs or reward models -- to restore visual fidelity. In this work, we introduce Continuous-Time Distribution Matching (CDM), migrating the DMD framework from discrete anchoring to continuous optimization for the first time. CDM achieves this through two continuous-time designs. First, we replace the fixed discrete schedule with a dynamic continuous schedule of random length, so that distribution matching is enforced at arbitrary points along sampling trajectories rather than only at a few fixed anchors. Second, we propose a continuous-time alignment objective that performs active off-trajectory matching on latents extrapolated via the student's velocity field, improving generalization and preserving fine visual details. Extensive experiments on different architectures, including SD3-Medium and Longcat-Image, demonstrate that CDM provides highly competitive visual fidelity for few-step image generation without relying on complex auxiliary objectives. Code is available at https://github.com/byliutao/cdm.

This position paper argues that understanding generalization in diffusion models requires fundamentally new theoretical frameworks that go beyond both classical statistical learning theory and the benign overfitting paradigm developed for supervised learning. In diffusion models, unlike in supervised learning, memorization of training data and generalization to novel samples are incompatible: a model that has fully memorized its training set generates copies rather than novel data. Several theoretical explanations for why practical diffusion models nevertheless generalize have been proposed, based on capacity limitations, implicit regularization from optimization, or architectural inductive biases, but their interactions remain unclear. We argue that the field should pivot from explaining why the diffusion models do not memorize to investigating what the model actually learns during pre-memorization phase. To highlight our stance, we conduct empirical study of diffusion models trained on CIFAR-10, and we distill the findings into concrete open questions that we believe are key to improve understanding of generalization in diffusion models.

Purely RGB-based vision models often fail to provide reliable cues in challenging scenarios such as nighttime and fog, leading to degraded performance and safety risks. Infrared imaging captures heat-emitting sources and provides critical complementary information, but existing high-fidelity fusion methods suffer from prohibitive latency, rendering them impractical for real-time edge deployment. To address this, we propose FusionProxy, a real-time image fusion module designed as a fully independent, plug-and-play component with diffusion level quality. FusionProxy exploits two complementary statistics of a teacher sample ensemble: per-pixel variance in raw image space, used to weight pixel-level supervision, and per-pixel variance inside frozen foundation backbones, used to route feature-level alignment spatially. Once trained, FusionProxy can be directly integrated into any visual perception system without joint optimization. Extensive experiments demonstrate that our method achieves superior performance on static recognition tasks and significantly enhances robustness in dynamic tasks, including closed-loop autonomous driving. Crucially, FusionProxy achieves real-time inference speeds on diverse platforms, from high-end GPUs to commodity hardware, providing a flexible and generalizable solution for all-day perception.

Current Chinese calligraphy generation methods suffer from poor stroke rendering and unrealistic ink morphology, resulting in outputs with limited visual fidelity and artistic fluidity. To address this problem, we propose \textbf{InkDiffuser}, a diffusion-based generative framework for one-shot Chinese calligraphy synthesis. To guarantee high-fidelity rendering, we introduce two core contributions: a high-frequency enhancement mechanism and a Differentiable Ink Structure (DIS) loss that explicitly regularizes ink morphology. Inspired by the observation that high-frequency information in individual samples typically carries contour details, we enhance content extraction by explicitly fusing high-frequency representations for more accurate font structure. Furthermore, we propose a differentiable ink structure loss that integrates differentiable morphological operations into the diffusion process. By allowing the model to learn an explicit decomposition of ink-trace structures, DIS facilitates fine-grained refinement of stroke contours and delivers significantly improved visual realism in the generated calligraphy. Extensive experiments on various calligraphic styles and complex characters demonstrate that InkDiffuser can generate superior calligraphy fonts with realistic ink rendering effects from only a single reference glyph and outperform existing few-shot font generation approaches in structural consistency, detail fidelity, and visual authenticity. The code is available at the following address: https://github.com/JingVIPLab/InkDiffuser.

Conditional generative models, particularly diffusion-based methods, have recently been applied to graph prediction by modeling the target as a conditional distribution given the input graph, yielding competitive results compared to deterministic predictor. However, existing diffusion-based prediction methods typically require expensive iterative denoising at inference and often suffer from unstable sampling, which motivates recent efforts to reduce inference denoising steps and enable stable sampling via techniques such as consistency training. Despite this progress, we find that existing consistency training methods for graph prediction could potentially fall into a shortcut solution: the model may attempt to satisfy the self-consistency constraint by ignoring the noisy target (i.e., assigning it negligible weight), ultimately collapsing into a purely deterministic predictor. To mitigate such shortcut solution, we propose GCCM, a graph contrastive consistency model that goes beyond isolated pairwise matching between the same target at different noise levels by introducing negative pairs into a contrastive consistency objective. This adds an additional separation requirement, making the shortcut solution no longer trivially sufficient to satisfy the proposed objective. Moreover, we apply feature perturbation to the input node/edge features to break identical conditioning on the input graph, so that the shortcut no longer yields the same predictions across noise levels and becomes less attractive. Extensive experiments on benchmark datasets demonstrate that GCCM mitigates the shortcut solution and yields consistent performance improvements in graph prediction compared to deterministic predictors.

RGB-to-hyperspectral image reconstruction is a highly ill-posed inverse problem, since multiple plausible spectral distributions may correspond to the same RGB observation. Existing regression-based methods usually learn a deterministic mapping, which limits their ability to model reconstruction uncertainty and often leads to over-smoothed spectral responses. Although diffusion models provide strong distribution modeling capability, their direct application to hyperspectral reconstruction remains challenging due to the high spectral dimensionality, strong inter-band correlations, and strict requirement for spectral fidelity. To this end, we propose R2H-Diff, an efficient diffusion-based framework tailored for RGB-to-HSI reconstruction. Specifically, R2H-Diff formulates spectral recovery as a conditional iterative refinement process, enabling progressive reconstruction under RGB guidance. We proposed a Guided Spectral Refinement Module for RGB-conditioned feature fusion and a Hyperspectral-Adaptive Transposed Attention module for efficient spatial--spectral dependency modeling. Furthermore, a normalization-free denoising backbone is adopted to preserve spectral amplitude consistency, while a task-adapted linear noise schedule enables high-quality reconstruction with only five denoising steps. Extensive experiments on NTIRE2022, CAVE, and Harvard demonstrate that R2H-Diff achieves a favorable balance between reconstruction quality and computational efficiency. Notably, on NTIRE2022, R2H-Diff obtains 35.37 dB PSNR with a sub-million-parameter model of 0.58M parameters and 12.25G FLOPs, achieving the lowest model complexity among the evaluated methods while maintaining strong reconstruction fidelity.

Diffusion models have recently achieved remarkable performance in image super-resolution (SR), but their high computational cost limits practical deployment in remote sensing applications. To address this issue, we propose SlimDiffSR, a lightweight and efficient diffusion-based framework for real-world remote sensing image super-resolution. Unlike existing single-step diffusion methods that rely on fixed timesteps, we first introduce an uncertainty-guided timestep assignment strategy to construct a stronger single-step teacher model, where reconstruction difficulty is explicitly linked to diffusion timesteps, enabling adaptive generative strength. Building upon this teacher, we further present a structured pruning strategy tailored to remote sensing imagery, which systematically removes redundant semantic modules and replaces standard operations with lightweight designs, including frequency-separable convolution, direction-separable convolution, and a query-driven global aggregation module. These components explicitly exploit the unique characteristics of remote sensing data, such as sparse high-frequency details, strong directional patterns, and long-range spatial dependencies. To enhance knowledge transfer, we incorporate Maximum Mean Discrepancy (MMD) into the distillation process to align feature distributions between the teacher and student models. Extensive experiments on multiple remote sensing benchmarks demonstrate that SlimDiffSR achieves a favorable balance between efficiency and reconstruction quality. In particular, it attains up to $200\times$ inference acceleration and a $20\times$ reduction in model parameters compared with multi-step diffusion models, while achieving competitive perceptual quality and clearly outperforming existing lightweight diffusion baselines in efficiency. The code is available at: https://github.com/wwangcece/SlimDiffSR.

Diffusion models (DMs) excel on dense continuous data, but are not designed for sparse continuous data. They do not model exact zeros that represent the deliberate absence of a signal. As a result, they erase sparsity patterns and perform unnecessary computation on mostly zero entries. With Sparsity-Exploiting Diffusion (SED), we model only non-zero values, preserving sparsity. SED delivers computational savings while maintaining or improving generation quality by skipping zeros during training and inference. Across physics and biology benchmarks, SED matches or surpasses conventional DMs and domain-specific baselines, while vision experiments provide intuitive insights into the limitations of dense DMs and the benefits of SED.

Most recent extreme rescaling methods struggle to preserve semantically consistent structures and produce realistic details, due to the severely ill-posed nature of low- to high-resolution mapping under scaling factors of $16\times$ or higher. To alleviate the above problems, we propose FaithEIR, a diffusion-based framework for extreme image rescaling. Inspired by singular value decomposition, we develop learnable reversible transformation that enables invertible downscaling and upscaling in the latent space. To compensate for information loss due to quantization, we propose an adaptive detail prior, a high-frequency dictionary that captures the empirical average of commonly occurring structures in the training data. Finally, we design a lightweight pixel semantic embedder to provide semantic conditioning for the pretrained diffusion model. We present extensive experimental results demonstrating that our FaithEIR consistently outperforms state-of-the-art methods, achieving superior reconstruction fidelity and perceptual quality. Our code, model weights, and detailed results are released at https://github.com/cshw2021/FaithEIR.

Accurate modeling of commuting flows is important for urban governance, traffic planning, and resource allocation. However, the combined influence of individual intentions, geographic constraints, and social dynamics leads to considerable heterogeneity in commuting patterns, making it difficult to develop generation models that generalize across cities. To address this issue, we propose SEDAN, a Structure-Enhanced Diffusion model conditioned on Attributed Nodes for generalizable OD matrix generation. SEDAN models a city as an attributed graph. Each region is treated as a node with demographic and point-of-interest features, and commuting flows are modeled as weighted edges. Adjacency and distance matrices are incorporated to characterize spatial structure. Based on this representation, we design a fusion mechanism within SEDAN to jointly model semantic information and spatial information. Regional semantic attributes are used to model latent travel demand through graph-transformer-based node interactions, while spatial structure is injected into the generation process as explicit constraints. The adjacency matrix guides attention weights to strengthen interactions between neighboring regions. Meanwhile, the distance matrix serves as a diffusion condition to capture spatial proximity and travel impedance. The fusion of urban semantics and spatial constraints enables SEDAN to generate OD matrices that are both behaviorally plausible and geographically coherent. Experiments on real-world OD datasets from U.S. cities show that SEDAN achieves a 7.38% improvement in RMSE over the state-of-the-art baseline, WEDAN. It also remains robust across heterogeneous urban scenarios and varying structural patterns. Our work provides an effective and generalizable solution for commuting OD matrix generation. The code is available at https://anonymous.4open.science/r/SEDAN.

Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting where common approaches focus on learning discrete scores and rates. In this work we close this gap for discrete non-negative ordinal data by introducing Binomial flows. Our framework provides a simple recipe for training a discrete diffusion model which simultaneously denoises, samples, and estimates exact likelihoods. We verify our methodology on synthetic examples and obtain competitive results on real-world data sets.

Many diffusion based molecule generation methods ignore the symbolic information of molecules and represent the atom and bond type as one hot representation. Methods based on Morgan fingerprints produce hash collisions and are hard to embed into a continuous space without information loss and random fingerprints correspond to no valid molecule. To circumvent this issue we use another paradigm and consider atom and bond codes as latent variables of VQ-VAE. We introduce VQ-SAD which first trains a VQ-VAE and uses the frozen pretrained VQ-VAE model and considers the codebooks for both atom and bond types as tokenizers for the downstream diffusion process. VQ-SAD is a neuro-symbolic model that utilizes both symbolic and neural structural information for a diffusion based model with learnable forward process. The large discrete code space provides a more balanced atom and bond types which enhances the denoising process. VQ-VAE slightly outperforms SOTA models for diffusion based molecule generation on QM9 and ZINC250k datasets.

Text-to-image diffusion models achieve impressive visual fidelity, yet they remain unreliable in multi-object generation. Despite extensive empirical evidence of these failures, the underlying causes remain unclear. We begin by asking how much of this limitation arises from the data itself. To disentangle data effects, we consider two regimes across different dataset sizes: (1) concept generalization, where each individual concept is observed during training under potentially imbalanced data distributions, and (2) compositional generalization, where specific combinations of concepts are systematically held out. To study these regimes, we introduce mosaic (Multi-Object Spatial relations, AttrIbution, Counting), a controlled framework for dataset generation. By training diffusion models on mosaic, we find that scene complexity plays a dominant role rather than concept imbalance, and that counting is uniquely difficult to learn in low-data regimes. Moreover, compositional generalization collapses as more concept combinations are held out during training. These findings highlight fundamental limitations of diffusion models and motivate stronger inductive biases and data design for robust multi-object compositional generation.

Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps. In continuous domains, consistency training along the probability-flow ODE is a popular recipe to accelerate diffusion. For discrete diffusion, no analogous sample-space ODE exists, making direct adaptation ill-defined. We argue that the right discrete substitute is the exact posterior bridge, the closed-form conditional law linking any two noise levels, which is available for broad corruptions including masked and uniform diffusion. Building on this observation, we introduce Multi-Path Discrete Consistency (MPDC), a new principle that trains a denoiser to be path-invariant in expectation across these stochastic bridges, and instantiate it as the Consistent Diffusion Language Model (CDLM), a single-stage training framework that does not require an already trained teacher model. Our CDLM objective recovers masked diffusion, continuous consistency models, and progressive or discrete distillation as analytic limits or empirical approximations of one common view. Empirically, CDLM establishes a new state of the art on both conditional and unconditional text-generation, consistently outperforming strong base discrete diffusion models and often even multi-stage distilled baselines across sampling budgets, with the largest gains in the few-step regime. Together, these results position CDLM as a principled and scalable foundation for the next generation of fast, high-fidelity discrete generative modeling.

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

3D shapes from scanning, reconstruction, or AI-generated content often lack simple quad mesh layouts -- critical for efficient editing and modeling. Existing quad-remeshing techniques typically produce complex layouts with irregular loops, leading to tedious manual cleanup and extensive algorithm tuning. We introduce SQuadGen, a diffusion-based generative framework that leverages Chart Distance Fields (CDF) to synthesize simple quad layouts on 3D shapes. Our approach addresses two key challenges: (1) the discrete nature of mesh connectivity, which hinders learning, and (2) the scarcity of large-scale datasets with simple quad meshes. To overcome the first, we propose CDF, a continuous surface-based representation enabling effective learning and synthesis of quad layouts. To address the second, we define loop-aware simplicity metrics and construct a large-scale dataset of high-quality quad layouts recovered from public 3D repositories through a robust quad-recovery pipeline. Extensive evaluations across diverse 3D inputs show that SQuadGen consistently outperforms existing methods, producing robust, artist-friendly simple quad layouts.

Data quality assessment is an essential step that ensures the reliability of the subsequent structural health monitoring (SHM) tasks. This study proposes a prediction deviation-based SHM data quality assessment method using a univariate implicit auto-regressive model, enabling outlier diagnosis and data cleaning. The proposed conditional diffusion model (CDM) augments the standard diffusion model with a conditional embedding module to incorporate temporal context, quartile normalization to mitigate distribution skew, and a Huber loss to enhance robustness against outliers. Within this univariate implicit autoregressive framework, each data point is assigned an outlier probability, quantifying its degree of "outlier-ness", and a global quality evaluation score is computed to characterize the overall dataset quality. Extensive case studies utilizing operational data from real-world structures demonstrate that the proposed framework significantly improves the accuracy of data quality assessment, outperforming other strong baselines representative of clustering, isolation-based, and deep reconstruction methods. The effectiveness and robustness of the proposed framework are further demonstrated by the findings of ablation experiments and hyperparameter analysis.

Masked diffusion models (MDMs) generate discrete sequences by iterative denoising under an absorbing masking process. In standard masked diffusion, if a token remains masked after a reverse update, the model discards its clean-state prediction for that position. Thus, still-masked positions must be repeatedly inferred from the mask token alone. This design choice limits cross-step refinement. To address this limitation, this paper proposes a simple, yet effective, post-training adaptation for MDMs that conditions each denoising step on the model's own previous clean-state predictions. The resulting method, called Self-Conditioned Masked Diffusion Models (SCMDM), requires minimal architectural change, does not introduce a recurrent latent-state pathway, does not rely on an auxiliary reference model, and adds no extra denoiser evaluations during sampling. This is an important departure from partial self-conditioning approaches which requires expensive model training from scratch. In particular, the paper shows that partial self-conditioning, including the commonly used 50% dropout strategy for training self-conditioned models from scratch, is suboptimal in the post-training regime. Instead, once the model's self-generated clean-state estimates become informative, the specialization to refinement is preferable to mixing conditional and unconditional objectives. SCMDM is evaluated across multiple domains, demonstrating consistent improvement over vanilla MDM baselines, achieving nearly a 50% reduction in generative perplexity on OWT-trained models (42.89 to 23.72), alongside strong improvements in discretized image synthesis quality, small molecular generation, and enhanced fidelity in genomic distribution modeling.

Diffusion models have achieved success in high-fidelity data synthesis, yet their capacity for more complex, structured reasoning like text following tasks remains constrained. While advances in language models have leveraged strategies such as latent reasoning and recursion to enhance text understanding capabilities, extending these to multimodal text-to-image generation tasks is challenging due to the continuous and non-discrete nature of visual tokens. To tackle this problem, we draw inspiration from modular human cognition and propose a recursive, sparse mixture-of-experts framework integrated into conventional diffusion models. Our approach introduces a recursive component within joint attention layers that iteratively refines visual tokens over multiple latent steps while efficiently sharing parameters via sparse selection of neural modules. At each step, a gating network is devised to dynamically select specialized neural modules, conditioned on the current visual tokens, the diffusion timestep, and the conditioning information. Comprehensive evaluation on class-conditioned ImageNet image generation tasks and additional studies on the GenEval and DPG benchmark demonstrate the superiority of the proposed method in enhancing model image generation performance.

Face swapping aims to optimize realistic facial image generation by leveraging the identity of a source face onto a target face while preserving pose, expression, and context. However, existing methods, especially GAN-based methods, often struggle to balance identity preservation and visual realism due to limited controllability and mode collapse. In this paper, we introduce CA-IDD (Cross-Attention Guided Identity-Conditional Diffusion), the first diffusion-based face swapping approach that integrates multi-modal guidance comprising gaze, identity, and facial parsing through multi-scale cross-attention. Precomputed identity embeddings are incorporated into the denoising process via hierarchical attention layers, resulting in accurate and consistent identity transfer. To improve semantic coherence and visual quality, we use expert-guided supervision, with facial parsing and gaze-consistency modules. Unlike GAN-based or implicit-fusion methods, our diffusion framework provides stable training, robust generalization, and spatially adaptive identity alignment, allowing for fine-grained regional control across pose and expression variations. CA-IDD achieves an FID of 11.73, exceeding established baselines such as FaceShifter and MegaFS. Qualitative results also reveal improved identity retention across diverse poses, establishing CA-IDD as a strong foundation for future diffusion-based face editing.

Diffusion models are central to modern generative modeling, and understanding how they balance memorization and generalization is critical for reliable deployment. Recent work has shown that memorization in diffusion models is shaped by training dynamics, with generalization and memorization emerging at different stages of training. However, deployed diffusion models are often further distilled, introducing an additional training phase whose impact on memorization is not well understood. In this work, we analyze how distillation reshapes memorization behavior in diffusion models, taking consistency distillation as a representative framework. Empirically, we show that when applied to a teacher model that has memorized data, consistency distillation significantly reduces transferred memorization in the student while preserving, and sometimes improving, sample quality. To explain this behavior, we provide a theoretical analysis using a random feature neural network model [Bonnaire et al., 2025], showing that consistency distillation suppresses unstable feature directions associated with memorization while preserving stable, generalizable modes. Our findings suggest that distillation can serve not only as an acceleration tool, but also as a mechanism for improving the memorization-generalization trade-off.

Multimodal Federated Learning (MMFL) enables privacy-preserving collaborative training, but real-world clinical applications often suffer from within-modality missingness caused by sensor intermittency or irregular sampling. Existing methods implicitly represent unobserved data via architectural alignment or missing embeddings, often failing to recover the true distribution and yielding sub-optimal performance. We propose CondI, a federated framework explicitly addressing this missingness using conditional diffusion models. CondI employs a two-phase training pipeline: first, imputing unobserved temporal components using available multimodal context and conditional embeddings; second, optimizing modality-specific extractors and joint embedding spaces. During inference, imputed raw data pass through trained extractors to generate robust features, providing a holistic representation for downstream tasks. Explicit data imputation ensures models operate on complete semantic structures, significantly enhancing resilience against severe data incompleteness. Experiments on three clinical datasets (PTB-XL, SLEEP-EDF, MIMIC-IV) demonstrate CondI achieves comparable results to state-of-the-art baselines. Code: https://github.com/ZhengWugeng/CondI

Understanding and predicting the progression of neurodegenerative diseases remains a major challenge in medical AI, with significant implications for early diagnosis, disease monitoring, and treatment planning. However, most available longitudinal neuroimaging datasets are temporally sparse with a few follow-up scans per subject. This scarcity of temporal data limits our ability to model and accurately capture the continuous anatomical changes related to disease progression in individual subjects. To address this problem, we propose a novel 4D (3DxT) diffusion-based generative framework that effectively models and synthesizes longitudinal brain anatomy over time, conditioned on available clinical variables such as health status, age, sex, and other relevant factors. Moreover, while most current approaches focus on manipulating image intensity or texture, our method explicitly learns the data distribution of topology-preserving spatiotemporal deformations to effectively capture the geometric changes of brain structures over time. This design enables the realistic generation of future anatomical states and the reconstruction of anatomically consistent disease trajectories, providing a more faithful representation of longitudinal brain changes. We validate our model through both synthetic sequence generation and downstream longitudinal disease classification, as well as brain segmentation. Experiments on two large-scale longitudinal neuroimage datasets demonstrate that our method outperforms state-of-the-art baselines in generating anatomically accurate, temporally consistent, and clinically meaningful brain trajectories. Our code is available on Github.

Objective: Decoding visual information from electroencephalography (EEG) is an important problem in neuroscience and brain-computer interface (BCI) research. Existing methods are largely restricted to natural images and categorical representations, with limited capacity to capture structural features and to differentiate objective perception from subjective cognition. We propose a Structure-Guided Diffusion Model (SGDM) that incorporates explicit structural information for EEG-based visual reconstruction. Approach: SGDM is evaluated on the Kilogram abstract visual object dataset and the THINGS natural image dataset using a two-stage generative mechanism. The framework combines a structurally supervised variational autoencoder with a spatiotemporal EEG encoder aligned to a visual embedding space via contrastive learning. Structural information is integrated into a diffusion model through ControlNet to guide image generation from EEG features. Results: SGDM outperforms existing methods on both abstract and natural image datasets. Reconstructed images achieve higher fidelity in low-level visual features and semantic representations, indicating improved decoding accuracy and strong generalization across diverse visual domains. Spatiotemporal analysis of EEG signals further reveals hierarchical structural encoding patterns, consistent with the neural dynamics of visual cognition. Significance: These findings validate the effectiveness of SGDM in capturing explicit structural geometry and generating images with high fidelity to individual cognitive representations. By enabling decoding of complex visual content from EEG signals, the framework extends neural decoding beyond low-dimensional or categorical outputs. This supports BCIs with increased degrees of freedom for intention decoding and more flexible brain-to-machine communication.

Diffusion models achieve remarkable success in time series generation. However, slow inference limits their practical deployment. We propose E$^2$-CRF (Error-Feedback Event-Driven Cumulative Residual Feature caching) to accelerate frequency domain diffusion models. Our method exploits two structural properties: (1) spectral localization, where signal energy concentrates in low frequencies, and (2) mirror symmetry, which halves the effective frequency dimension. E$^2$-CRF uses a closed-loop error-feedback system that adaptively caches transformer KV features across diffusion steps. We trigger recomputation using event-driven residual dynamics instead of fixed schedules. Our method selectively recomputes high-energy or rapidly-changing tokens while reusing cached features for stable high-frequency components. E$^2$-CRF achieves ~2.2 speedup while maintaining sample quality. We demonstrate effectiveness on 5 datasets. Our caching strategy naturally aligns with the diffusion process's structure-to-detail progression. We include sufficient-condition error and complexity bounds under standard regularity assumptions (Appendix), alongside empirical validation. Our code is available at https://github.com/NoakLiu/FastFourierDiffusion and is also integrated in https://github.com/NoakLiu/FastCache-xDiT.

Recent advances in distilling expensive diffusion models into efficient few-step generators show significant promise. However, these methods typically demand substantial computational resources and extended training periods, limiting accessibility for resource-constrained researchers, and existing supplementary loss functions have notable limitations. Regression loss requires pre-generating large datasets before training and limits the student model to the teacher's performance, while GAN-based losses suffer from training instability and require careful tuning. In this paper, we propose Embedding Loss (EL), a novel supplementary loss function that complements existing diffusion distillation methods to enhance generation quality and accelerate training with smaller batch sizes. Leveraging feature embeddings from a diverse set of randomly initialized networks, EL effectively aligns the feature distributions between the distilled few-step generator and the original data. By computing Maximum Mean Discrepancy (MMD) in the embedded feature space, EL ensures robust distribution matching, thereby preserving sample fidelity and diversity during distillation. Within distribution matching distillation frameworks, EL demonstrates strong empirical performance for one-step generators. On the CIFAR-10 dataset, our approach achieves state-of-the-art FID values of 1.475 for unconditional generation and 1.380 for conditional generation. Beyond CIFAR-10, we further validate EL across multiple benchmarks and distillation methods, including ImageNet, AFHQ-v2, and FFHQ datasets, using DMD, DI, and CM distillation frameworks, demonstrating consistent improvements over existing one-step distillation methods. Our method also reduces training iterations by up to 80%, offering a more practical and scalable solution for deploying diffusion-based generative models in resource-constrained environments.

Digital image watermarking has advanced rapidly for copyright protection of generative AI, yet the comparatively limited progress in watermark attack techniques has broken the attack-defense balance and hindered further advances in the field. In this paper, we propose FMDiffWA, a frequency-domain modulated diffusion framework for watermark attacks. Specifically, we introduce a frequency-domain watermark modulation (FWM) module and incorporate it into the sampling stages both the forward and reverse diffusion processes. This mechanism enables selective modulation of watermark-related frequency components, thereby allowing FMDiffWA to effectively neutralize the invisible watermark signals while preserving the perceptual quality of the attacked watermarked images. To achieve a better trade-off between attack efficacy and visual fidelity, we reformulate the training strategy of conventional diffusion models by augmenting the canonical noise estimation objective with an auxiliary refinement constraint. Comprehensive experiments demonstrate that FMDiffWA achieves superior visual fidelity compared to existing watermark attacks, while exhibiting strong generalization across diverse watermarking schemes.

Facial attribute editing aims to modify target attributes while preserving attribute-irrelevant content and overall image fidelity. Existing GAN-based methods provide favorable controllability, but often suffer from weak alignment between style codes and attribute semantics. Diffusion-based methods can synthesize highly realistic images; however, their editing precision is limited by the entanglement of semantic directions among different attributes. In this paper, we propose AttDiff-GAN, a hybrid framework that combines GAN-based attribute manipulation with diffusion-based image generation. A key challenge in such integration lies in the inconsistency between one-step adversarial learning and multi-step diffusion denoising, which makes effective optimization difficult. To address this issue, we decouple attribute editing from image synthesis by introducing a feature-level adversarial learning scheme to learn explicit attribute manipulation, and then using the manipulated features to guide the diffusion process for image generation, while also removing the reliance on semantic direction-based editing. Moreover, we enhance style-attribute alignment by introducing PriorMapper, which incorporates facial priors into style generation, and RefineExtractor, which captures global semantic relationships through a Transformer for more precise style extraction. Experimental results on CelebA-HQ show that the proposed method achieves more accurate facial attribute editing and better preservation of non-target attributes than state-of-the-art methods in both qualitative and quantitative evaluations.

In continuously monitored quantum systems, the feedback protocol of García-Pintos, Liu, and Gorshkov reshapes the arrow of time: a Hamiltonian $H_{\mathrm{meas}} = r A / τ$ applied with gain $X$ tilts the distribution of measurement trajectories, with $X < -2$ producing statistically time-reversed outcomes. Why this specific Hamiltonian achieves reversal, and how the mechanism relates to score-based diffusion models in machine learning, has remained unexplained. We compute the functional derivative of the log path probability of the quantum trajectory distribution directly in density-matrix space. Combining Girsanov's theorem applied to the measurement record, Fréchet differentiation on the Banach space of trace-class operators, and Kähler geometry on the pure-state projective manifold, we prove that $δ\log P_F / δρ= r A / τ= H_{\mathrm{meas}}$. The García-Pintos feedback Hamiltonian is the score function of the quantum trajectory distribution -- exactly the object Anderson's reverse-time diffusion theorem requires for trajectory reversal. The identification extends to multi-qubit systems with independent measurement channels, where the score is a sum of local operators. Two consequences follow. First, the feedback gain $X$ generates a continuous one-parameter family of path measures (for feedback-active Hamiltonians with $[H, A] \neq 0$), with $X = -2$ recovering the backward process in leading-order linearization -- a structure absent from classical diffusion, where reversal is binary. Second, the score identification enables machine learning (ML) score estimation methods -- denoising score matching, sliced score matching -- to replace the analytic formula when its idealizations (unit efficiency, zero delay, Gaussian noise) fail in real experiments.

Forecasting the life-cycle trajectory of a newly launched product is important for launch planning, resource allocation, and early risk assessment. This task is especially difficult in the pre-launch and early post-launch phases, when product-specific outcome history is limited or unavailable, creating a cold-start problem. In these phases, firms must make decisions before demand patterns become reliably observable, while early signals are often sparse, noisy, and unstable We propose the Conditional Diffusion Life-cycle Forecaster (CDLF), a conditional generative framework for forecasting new-product life-cycle trajectories under cold start. CDLF combines three sources of information: static descriptors, reference trajectories from similar products, and newly arriving observations when available. Here, static descriptors refer to structured pre-launch characteristics of the product, such as category, price tier, brand or organization identity, scale, and access conditions. This structure allows the model to condition forecasts on relevant product context and to update them adaptively over time without retraining, yielding flexible multi-modal predictive distributions under extreme data scarcity. The method satisfies consistency with a horizon-uniform distributional error bound for recursive generation. Across studies on Intel microprocessor stock keeping unit (SKU) life cycles and the platform-mediated adoption of open large language model repositories, CDLF delivers more accurate point forecasts and higher-quality probabilistic forecasts than classical diffusion models, Bayesian updating approaches, and other state-of-the-art machine-learning baselines.

Accurate medical image segmentation requires both long-range contextual reasoning and precise boundary delineation, a task where existing transformer- and diffusion-based paradigms are frequently bottlenecked by quadratic computational complexity and prohibitive inference latency. We propose RF-HiT, a Rectified Flow Hierarchical Transformer that integrates an Hourglass Transformer backbone with a multi-scale hierarchical encoder for anatomically guided feature conditioning. Unlike prior diffusion-based approaches that rely on hundreds of denoising steps, RF-HiT leverages rectified flow with efficient transformer blocks, achieving linear complexity and requiring only a few discretization steps. The model further fuses conditioning features at each resolution via learnable interpolation, enabling effective multi-scale feature integration with minimal computational overhead. As a result, RF-HiT achieves a strong efficiency-performance trade-off, requiring only 10.14 GFLOPs, 13.6M parameters, and inference in as few as 3 steps. Despite its compact design, RF-HiT attains 91.27% mean Dice on ACDC and 87.40% on BraTS 2021, achieving performance comparable to or exceeding that of significantly more intensive architectures. These results suggest that RF-HiT is a promising, computationally efficient foundation for clinical image segmentation.

Satellite image composition plays a critical role in remote sensing applications such as data augmentation, disaste simulation, and urban planning. We propose HarmoniDiff-RS, a training-free diffusion-based framework for harmonizing composite satellite images under diverse domain conditions. Our method aligns the source and target domains through a Latent Mean Shift operation that transfers radiometric characteristics between them. To balance harmonization and content preservation, we introduce a Timestep-wise Latent Fusion strategy by leveraging early inverted latents for high harmonization and late latents for semantic consistency to generate a set of composite candidates. A lightweight harmony classifier is trained to further automatically select the most coherent result among them. We also construct RSIC-H, a benchmark dataset for satellite image harmonization derived from fMoW, providing 500 paired composition samples. Experiments demonstrate that our method effectively performs satellite image composition, showing strong potential for scalable remote-sensing synthesis and simulation tasks. Code is available at: https://github.com/XiaoqiZhuang/HarmoniDiff-RS.

Diffusion models have achieved outstanding performance in unsupervised industrial anomaly detection (uIAD) by learning a manifold of normal data under the common assumption that off-manifold anomalies are harder to generate, resulting in larger reconstruction errors in data space or lower probability densities in the tractable latent space. However, their iterative denoising and noising nature leads to slow inference. In this paper, we propose OSD-IRF, a novel one-step diffusion with inverse residual fields, to address this limitation for uIAD task. We first train a deep diffusion probabilistic model (DDPM) on normal data without any conditioning. Then, for a test sample, we predict its inverse residual fields (IRF) based on the noise estimated by the well-trained parametric noise function of the DDPM. Finally, uIAD is performed by evaluating the probability density of the IRF under a Gaussian distribution and comparing it with a threshold. Our key observation is that anomalies become distinguishable in this IRF space, a finding that has seldom been reported in prior works. Moreover, OSD-IRF requires only single step diffusion for uIAD, thanks to the property that IRF holds for any neighboring time step in the denoising process. Extensive experiments on three widely used uIAD benchmarks show that our model achieves SOTA or competitive performance across six metrics, along with roughly a 2X inference speedup without distillation.

Knowledge Graphs (KGs) are composed of triples, and the goal of Knowledge Graph Completion (KGC) is to infer the missing factual triples. Traditional KGC tasks predict missing elements in a triple given one or two of its elements. As a more realistic task, the Triple Set Prediction (TSP) task aims to infer the set of missing triples conditioned only on the observed knowledge graph, without assuming any partial information about the missing triples. Existing TSP methods predict the set of missing triples in a triple-by-triple manner, falling short in capturing the dependencies among the predicted triples to ensure consistency. To address this issue, we propose a novel discrete diffusion model termed DiffTSP that treats TSP as a generative task. DiffTSP progressively adds noise to the KG through a discrete diffusion process, achieved by masking relational edges. The reverse process then gradually recovers the complete KG conditioned on the incomplete graph. To this end, we design a structure-aware denoising network that integrates a relational context encoder with a relational graph diffusion transformer for knowledge graph generation. DiffTSP can generate the complete set of triples in a one-pass manner while ensuring the dependencies among the predicted triples. Our approach achieves state-of-the-art performance on three public datasets. Code: https://github.com/ADMIS-TONGJI/DiffTSP.

Diffusion-based image synthesis has emerged as a promising source of synthetic training data for AI-based object detection and classification. In this work, we investigate whether images generated with diffusion can improve military vehicle detection under low-data conditions. We fine-tuned the text-to-image diffusion model FLUX.1 [dev] using LoRA with only 8 or 24 real images per class across 15 vehicle categories, resulting in class-specific diffusion models, which were used to generate new samples from automatically generated text prompts. The same real images were used to fine-tune the RF-DETR detector for a 15-class object detection task. Synthetic datasets generated by the diffusion models were then used to further improve detector performance. Importantly, no additional real data was required, as the generative models leveraged the same limited training samples. FLUX-generated images improved detection performance, particularly in the low-data regime (up to +8.0% mAP$_{50}$ with 8 real samples). To address the limited geometric control of text prompt-based diffusion, we additionally generated structurally guided synthetic data using ControlNet with Canny edge-map conditioning, yielding a FLUX-ControlNet (FLUX-CN) dataset with explicit control over viewpoint and pose. Structural guidance further enhanced performance when data is scarce (+4.1% mAP$_{50}$ with 8 real samples), but no additional benefit was observed when more real data is available. This study demonstrates that object-specific diffusion models are effective for improving military object detection in a low-data domain, and that structural guidance is most beneficial when real data is highly limited. These results highlight generative image data as an alternative to traditional simulation pipelines for the training of military AI systems.

Despite their empirical success, how diffusion models generalize remains poorly understood from a mechanistic perspective. We demonstrate that diffusion models trained with flow-matching objectives exhibit grokking--delayed generalization after overfitting--on modular addition, enabling controlled analysis of their internal computations. We study this phenomenon across two levels of data regime. In a single-image regime, mechanistic dissection reveals that the model implements modular addition by composing periodic representations of individual operands. In a diverse-image regime with high intraclass variability, we find that the model leverages its iterative sampling process to partition the task into an arithmetic computation phase followed by a visual denoising phase, separated by a critical timestep threshold. Our work provides the mechanistic decomposition of algorithmic learning in diffusion models, revealing how these models bridge continuous pixel-space generation and discrete symbolic reasoning.

Discrete diffusion models form a powerful class of generative models across diverse domains, including text and graphs. However, existing approaches face fundamental limitations. Masked diffusion models suffer from irreversible errors due to early unmasking, while uniform diffusion models, despite enabling self-correction, often yield low-quality samples due to their strong reliance on intermediate latent states. We introduce IDDM, an Interpolating Discrete Diffusion Model, that improves diffusion by reducing dependence on intermediate latent states. Central to IDDM is a controllable resampling mechanism that partially resets probability mass to the marginal distribution, mitigating error accumulation and enabling more effective token corrections. IDDM specifies a generative process whose transitions interpolate between staying at the current state, resampling from a prior, and flipping toward the target state, while enforcing marginal consistency and fully decoupling training from inference. We benchmark our model against state-of-the-art discrete diffusion models across molecular graph generation as well as text generation tasks, demonstrating competitive performance.

We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a bi-level optimization approach for the dual-arm problem, where we derived the analytical solution to the lower-level convex sub-problem and solved the high-level nonconvex problem using a primal-dual approach. However, the gradient-based nature leads to a large computation overhead, and it prohibits directly imposing an $L_{\infty}$ Cartesian error constraint along the joint trajectory due to the sparsity of the gradient. In this work, we propose a diffusion-based framework that relies on probabilistic sampling to tackle the aforementioned challenges in the nonconvex high-level problem, leading to a 35x reduction in the runtime and 34% less Cartesian error compared to our prior work.

Tone style transfer for photo retouching aims to adapt the stylistic tone of the reference image to a given content image. However, the lack of high-quality large-scale triplet datasets with stylized ground truth forces existing methods to rely on self-supervised or proxy objectives, which limits model capability. To mitigate this gap, we design a data construction pipeline to build TST100K, a large-scale dataset of 100,000 content-reference-stylized triplets. At the core of this pipeline, we train a tone style scorer to ensure strict stylistic consistency for each triplet. In addition, existing methods typically extract content and reference features independently and then fuse them in a decoder, which may cause semantic loss and lead to inappropriate color transfer and degraded visual aesthetics. Instead, we propose ICTone, a diffusion-based framework that performs tone transfer in an in-context manner by jointly conditioning on both images, leveraging the semantic priors of generative models for semantic-aware transfer. Reward feedback learning using the tone style scorer is further incorporated to improve stylistic fidelity and visual quality. Experiments demonstrate the effectiveness of TST100K, and ICTone achieves state-of-the-art performance on both quantitative metrics and human evaluations.

Discrete diffusion models based on continuous-time Markov chains (CTMCs) have shown strong performance on language and discrete data generation, yet existing approaches typically parameterize the reverse rate matrix monolithically -- through proxies such as concrete scores (SEDD) or clean-data predictions (MDLM, GIDD) -- rather than aligning the parameterization with the intrinsic CTMC decomposition into jump timing and jump direction. We propose \textbf{Neural CTMC}, which exploits the underlying Poisson structure of CTMC dynamics by separately parameterizing the reverse process through an \emph{exit rate} (when to jump) and a \emph{jump distribution} (where to jump) via two dedicated network heads. We show that the evidence lower bound (ELBO) reduces to a path-space KL divergence between the true and learned reverse processes that factorizes into a Poisson KL for timing and a categorical KL for direction, and admits a tractable, gradient-equivalent and consistent loss. Experimentally, scored by Gemma2-9B, our pure-uniform Neural CTMC achieves $16.36$ generative perplexity on TinyStories (vs.\ GIDD $37.60$ and MDLM $42.66$). On OpenWebText, it attains the best perplexity at the same training-token budget across 16--128 sampling steps among the methods we compare (e.g., at 128 steps: Neural CTMC $183.6$ vs.\ MDLM $210.5$ and GIDD $249.8$). To facilitate reproducibility, we release our pretrained weights at https://huggingface.co/Jiangxy1117/Neural-CTMC.

Human activity traces (HATs) are critical for many applications, including human mobility modeling and point-of-interest (POI) recommendation. However, growing privacy concerns have severely limited access to authentic large-scale HAT datasets. Recent advances in generative AI provide new opportunities to synthesize realistic and privacy-preserving HATs for such applications. Yet two major challenges remain: (i) HATs are highly irregular and dynamic, with long and varying time intervals, making it difficult to capture their complex spatio-temporal dependencies and underlying distributions; and (ii) generative models are often computationally expensive, making long-term, fine-grained HAT synthesis inefficient. To address these challenges, we propose SynHAT, a computationally efficient coarse-to-fine HAT synthesis framework built on a novel spatio-temporal denoising diffusion model. In Stage 1, we develop Coarse-HADiff, which models the overall spatio-temporal dependencies of coarse-grained latent spatio-temporal traces. It incorporates a novel Latent Spatio-Temporal U-Net with dual Drift-Jitter branches to jointly model smooth spatial transitions and temporal variations during denoising. In Stage 2, we introduce a three-step pipeline consisting of Behavior Pattern Extraction, Fine-HADiff, which shares the same architecture as Coarse-HADiff, and Semantic Alignment to generate fine-grained latent spatio-temporal traces from the Stage 1 outputs. We extensively evaluate SynHAT in terms of data fidelity, utility, privacy, robustness, and scalability. Experiments on real-world HAT datasets from four cities across three countries show that SynHAT substantially outperforms state-of-the-art baselines, achieving 52% and 33% improvements on spatial and temporal metrics, respectively.

We study the classification task of structured-light beams after propagation through a random turbulent medium. The received speckle patterns are generated by numerical simulation of a stochastic paraxial propagation model, and the classification task is formulated over a finite alphabet of 15 OAM source classes. We benchmark intensity and autocorrelation inputs using SimpleCNN and ResNet-18 as classifiers. We also quantify the effect of training-set size and receiver-window misalignment. Since additional propagated samples may be costly to obtain, we develop a class-conditioned diffusion model for generative augmentation of turbulence-degraded intensity images. The main contribution is a spectrum-aware diffusion objective: a pixel-domain loss combined with a Fourier-domain Bregman regularizer designed to preserve high-frequency speckle statistics. We prove that this hybrid objective is consistent with the posterior-mean regression target of the diffusion model and show that generated samples substantially improve low-data classification.

We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature neural network. We derive asymptotically exact expressions for the test, train, and score errors in the high-dimensional limit. Our analysis reveals that, for linear manifolds the sample complexity required to learn the score function scales linearly with the intrinsic dimension of the manifold, rather than with the ambient dimension. Perhaps surprisingly, the benefits of low-dimensional structure starts to diminish once we have a non-linear manifold. These results indicate that diffusion models can benefit from structured data; however, the dependence on the specific type of structure is subtle and intricate.

Class-conditional generative models have emerged as accurate and robust classifiers, with diffusion models demonstrating clear advantages over other visual generative paradigms, including autoregressive (AR) models. In this work, we revisit visual AR-based generative classifiers and identify an important limitation of prior approaches: their reliance on a fixed token order, which imposes a restrictive inductive bias for image understanding. We observe that single-order predictions rely more on partial discriminative cues, while averaging over multiple token orders provides a more comprehensive signal. Based on this insight, we leverage recent any-order AR models to estimate order-marginalized predictions, unlocking the high classification potential of AR models. Our approach consistently outperforms diffusion-based classifiers across diverse image classification benchmarks, while being up to 25x more efficient. Compared to state-of-the-art self-supervised discriminative models, our method delivers competitive classification performance - a notable achievement for generative classifiers.

Ambiguous 3D medical image segmentation often involves boundaries where different expert delineations are non-identical yet clinically plausible. Modeling such inter-observer variability requires a careful balance between diversity and anatomical fidelity: deterministic models preserve coherent volumetric structures but collapse expert disagreement into a single mask, while stochastic generative models can produce diverse samples but may introduce disconnected components or slice-to-slice inconsistency when generating full 3D masks from unstructured noise. We propose Volumetric Directional Diffusion (VDD), a prior-anchored diffusion framework that shifts stochastic generation from full-mask synthesis to residual boundary exploration. VDD uses a coarse consensus prediction as an anatomical anchor and learns a directional diffusion process to generate plausible boundary variations around ambiguous regions while preserving stable volumetric topology. Experiments on three multi-rater datasets, including LIDC-IDRI, KiTS21, and ISBI 2015, show that VDD improves uncertainty distribution alignment while maintaining competitive segmentation accuracy and 3D structural consistency. These results suggest that prior-anchored residual diffusion can model clinically plausible expert disagreement without sacrificing anatomical fidelity.

Diffusion models over discrete spaces have recently shown striking empirical success, yet their theoretical foundations remain incomplete. In this paper, we study the sampling efficiency of score-based discrete diffusion models under a continuous-time Markov chain (CTMC) formulation, with a focus on $τ$-leaping-based samplers. We establish sharp convergence guarantees for attaining $\varepsilon$ accuracy in Kullback-Leibler (KL) divergence for both uniform and masking noising processes. For uniform discrete diffusion, we show that the $τ$-leaping algorithm achieves an iteration complexity of order $\tilde O(d/\varepsilon)$, with $d$ the ambient dimension of the target distribution, eliminating linear dependence on the vocabulary size $S$ and improving existing bounds by a factor of $d$; moreover, we establish a matching algorithmic lower bound showing that linear dependence on the ambient dimension is unavoidable in general. For masking discrete diffusion, we introduce a modified $τ$-leaping sampler whose convergence rate is governed by an intrinsic information-theoretic quantity, termed the effective total correlation, which is bounded by $d \log S$ but can be sublinear or even constant for structured data. As a consequence, the sampler provably adapts to low-dimensional structure without prior knowledge or algorithmic modification, yielding sublinear convergence rates for various practical examples (such as hidden Markov models, image data, and random graphs). Our analysis requires no boundedness or smoothness assumptions on the score estimator beyond control of the score entropy loss.

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

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

Diffusion models have seen widespread adoption for text-driven human motion generation and related tasks due to their impressive generative capabilities and flexibility. However, current motion diffusion models face two major limitations: a representational gap caused by pre-trained text encoders that lack motion-specific information, and error propagation during the iterative denoising process. This paper introduces Reconstruction-Anchored Diffusion Model (RAM) to address these challenges. First, RAM leverages a motion latent space as intermediate supervision for text-to-motion generation. To this end, RAM co-trains a motion reconstruction branch with two key objective functions: self-regularization to enhance the discrimination of the motion space and motion-centric latent alignment to enable accurate mapping from text to the motion latent space. Second, we propose Reconstructive Error Guidance (REG), a testing-stage guidance mechanism that exploits the motion diffusion model's inherent self-correction ability to mitigate error propagation. At each denoising step, REG uses the motion reconstruction branch to reconstruct the previous estimate, reproducing the prior error patterns. By amplifying the residual between the current prediction and the reconstructed estimate, REG highlights the improvements in the current prediction. Extensive experiments demonstrate that RAM achieves significant improvements and state-of-the-art performance. Our code will be released.

Low-shot object counting addresses estimating the number of previously unobserved objects in an image using only few or no annotated test-time exemplars. A considerable challenge for modern low-shot counters are dense regions with small objects. While total counts in such situations are typically well addressed by density-based counters, their usefulness is limited by poor localization capabilities. This is better addressed by point-detection-based counters, which are based on query-based detectors. However, due to limited number of pre-trained queries, they underperform on images with very large numbers of objects, and resort to ad-hoc techniques like upsampling and tiling. We propose CoDi, the first latent diffusion-based low-shot counter that produces high-quality density maps on which object locations can be determined by non-maxima suppression. Our core contribution is the new exemplar-based conditioning module that extracts and adjusts the object prototypes to the intermediate layers of the denoising network, leading to accurate object location estimation. On FSC benchmark, CoDi outperforms state-of-the-art by 15% MAE, 13% MAE and 10% MAE in the few-shot, one-shot, and reference-less scenarios, respectively, and sets a new state-of-the-art on MCAC benchmark by outperforming the top method by 38% MAE. The code is available at https://github.com/gsustar/CoDi

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

The rapid growth in wireless infrastructure has increased the need to accurately estimate and forecast electromagnetic field (EMF) levels to ensure ongoing compliance, assess potential health impacts, and support efficient network planning. While existing studies rely on univariate forecasting of wideband aggregate EMF data, multivariate narrow-band EMF forecasting is needed to capture the inter-operator and inter-frequency variations essential for proactive network planning. To this end, this paper introduces EMFusion, a conditional diffusion-based EMF forecasting framework that integrates diverse contextual factors, such as time of day, season, and holidays, while providing uncertainty-aware probabilistic forecasts. The proposed architecture features a residual U-Net backbone enhanced by a cross-attention mechanism that dynamically integrates external conditions to guide the generation process. Furthermore, EMFusion integrates an imputation-based sampling strategy that treats forecasting as a structural inpainting task, ensuring temporal coherence even with irregular measurements. Unlike standard point forecasters, EMFusion generates empirical probabilistic prediction intervals from the learned conditional distribution, providing uncertainty-aware probabilistic forecasting rather than simple point estimation. Numerical experiments conducted on the multivariate narrow-band EMF datasets demonstrate that EMFusion with the contextual information of working hours outperforms the baseline models with or without conditions. The proposed EMFusion outperforms the best baseline by 23.85% in continuous ranked probability score (CRPS) and 13.93% in normalized root mean square error.