Diffusion-based generative models have long depended on Gaussian priors, with little exploration of alternative distributions. We introduce a Proper Hölder-Kullback Dirichlet framework that uses time-varying multiplicative transformations to define both forward and reverse diffusion processes. Moving beyond conventional reweighted evidence lower bounds (ELBO) or Kullback-Leibler upper bounds (KLUB), we propose two novel divergence measures: the Proper Hölder Divergence (PHD) and the Proper Hölder-Kullback (PHK) divergence, the latter designed to restore symmetry missing in existing formulations. When optimizing our Dirichlet diffusion model with PHK, we achieve a Fréchet Inception Distance (FID) of 2.78 on unconditional CIFAR-10. Comprehensive experiments on natural-image datasets validate the generative strengths of model and confirm PHK's effectiveness in model training. These contributions expand the diffusion-model family with principled non-Gaussian processes and effective optimization tools, offering new avenues for versatile, high-fidelity generative modeling.

Information diffusion prediction, which aims to forecast the future infected users during the information spreading process on social platforms, is a challenging and critical task for public opinion analysis. With the development of social platforms, mass communication has become increasingly widespread. However, most existing methods based on GNNs and sequence models mainly focus on structural and temporal patterns in social networks, suffering from spurious diffusion connections and insufficient information for diffusion analysis. We leverage the strong reasoning capabilities of LLMs and develop an LLM-based causal framework for diffusion influence derivation, named MILD. By comprehensively integrating four key factors of social diffusion--i.e., connections, active timelines, user profiles, and comments--MILD causally infers authentic diffusion links to construct a diffusion influence graph, GI. To validate the quality and reliability of our constructed graph GI, we propose a newly designed set of evaluation metrics for diffusion prediction. In experiments, MILD provides a reliable information diffusion structure that achieves an absolute improvement of 12% over the social network structure and achieves state-of-the-art performance in diffusion prediction. MILD is expected to contribute to higher-quality, more explainable, and more trustworthy public opinion analysis. The code and data are available at: https://github.com/Shang-hub/

Diffusion bridges are a promising class of deep-learning methods for sampling from unnormalized distributions. Recent works show that the Log Variance (LV) loss consistently outperforms the reverse Kullback-Leibler (rKL) loss when using the reparametrization trick to compute rKL-gradients. While the on-policy LV loss yields identical gradients to the rKL loss when combined with the log-derivative trick for diffusion samplers with non-learnable forward processes, this equivalence does not hold for diffusion bridges or when diffusion coefficients are learned. Based on this insight we argue that for diffusion bridges the LV loss does not represent an optimization objective that can be motivated like the rKL loss via the data processing inequality. Our analysis shows that employing the rKL loss with the log-derivative trick (rKL-LD) does not only avoid these conceptual problems but also consistently outperforms the LV loss. Experimental results with different types of diffusion bridges on challenging benchmarks show that samplers trained with the rKL-LD loss achieve better performance. From a practical perspective we find that rKL-LD requires significantly less hyperparameter optimization and yields more stable training behavior.1

Generating realistic time series samples is crucial for stress-testing models and protecting applications, user these privac samples y by using must synthetic meet certain data.

Masked diffusion models (MDM) are powerful generative models for discrete data that generate samples by progressively unmasking tokens in a sequence. Each token can take one of two states: masked or unmasked. We observe that token sequences often remain unchanged between consecutive sampling steps; consequently, the model repeatedly processes identical inputs, leading to redundant computation. To address this inefficiency, we propose the Partial masking scheme (Prime), which augments MDM by allowing tokens to take intermediate states interpolated between the masked and unmasked states. This design enables the model to make predictions based on partially observed token information, and facilitates a fine-grained denoising process. We derive a variational training objective and introduce a simple architectural design to accommodate intermediate-state inputs. Our method demonstrates superior performance across a diverse set of generative modeling tasks. On text data, it achieves a perplexity of 15.36 on OpenWebText, outperforming previous MDM (21.52), autoregressive models (17.54), and their hybrid variants (17.58), without relying on an autoregressive formulation.

Diffusion models have emerged as a promising alternative to autoregressive models in modeling discrete categorical data. However, diffusion models that directly work on discrete data space fail to fully exploit the power of iterative refinement, as the signals are lost during transitions between discrete states. Existing continuous diffusion models for discrete data underperform compared to discrete methods, and the lack of a clear connection between the two approaches hinders the development of effective diffusion models for discrete data. In this work, we propose a continuous diffusion model for language modeling that incorporates the geometry of the underlying categorical distribution. We establish a connection between the discrete diffusion and continuous flow on the statistical manifold, and building on this analogy, introduce a simple diffusion process that generalizes existing discrete diffusion models. We further propose a simulation-free training framework based on radial symmetry, along with a simple technique to address the high dimensionality of the manifold. Comprehensive experiments on language modeling benchmarks and other modalities show that our method outperforms existing discrete diffusion models and approaches the performance of autoregressive models. The code is available at https://github.com/harryjo97/RDLM.

Dataset distillation seeks to condense datasets into smaller but highly representative synthetic samples. While diffusion models now lead all generative benchmarks, current distillation methods avoid them and rely instead on GANs or autoencoders, or, at best, sampling from a fixed diffusion prior. This trend arises because naive backpropagation through the long denoising chain leads to vanishing gradients, which prevents effective synthetic sample optimization. To address this limitation, we introduce Latent Dataset Distillation with Diffusion Models (LD3M), the first method to learn gradient-based distilled latents and class embeddings endto-end through a pre-trained latent diffusion model. A linearly decaying skip connection, injected from the initial noisy state into every reverse step, preserves the gradient signal across dozens of timesteps without requiring diffusion weight fine-tuning. Across multiple ImageNet subsets at 128 128and 256 256, LD3M improves downstream accuracy by up to 4.8 percentage points (1 IPC) and 4.2 points (10 IPC) over the prior state-of-the-art.

Robustness to modeling errors and uncertainties remains a central challenge in reinforcement learning (RL). In this work, we address this challenge by leveraging diffusion models to train robust RL policies. Diffusion models have recently gained popularity in model-based RL due to their ability to generate full trajectories "all at once", mitigating the compounding errors typical of step-by-step transition models. Moreover, they can be conditioned to sample from specific distributions, making them highly flexible. We leverage conditional sampling to learn policies that are robust to uncertainty in environment dynamics. Building on the established connection between Conditional Value at Risk (CVaR) optimization and robust RL, we introduce Adversarial Diffusion for Robust Reinforcement Learning (AD-RRL). AD-RRL guides the diffusion process to generate worst-case trajectories during training, effectively optimizing the CVaR of the cumulative return. Empirical results across standard benchmarks show that AD-RRL achieves superior robustness and performance compared to existing robust RL methods.

Diffusion models show promise for dynamic scene deblurring; however, existing studies often fail to leverage the intrinsic nature of the blurring process within diffusion models, limiting their full potential. To address it, we present a Blur Diffusion Model (BlurDM), which seamlessly integrates the blur formation process into diffusion for image deblurring. Observing that motion blur stems from continuous exposure, BlurDM implicitly models the blur formation process through a dual-diffusion forward scheme, diffusing both noise and blur onto a sharp image. During the reverse generation process, we derive a dual denoising and deblurring formulation, enabling BlurDM to recover the sharp image by simultaneously denoising and deblurring, given pure Gaussian noise conditioned on the blurred image as input. Additionally, to efficiently integrate BlurDM into deblurring networks, we perform BlurDM in the latent space, forming a flexible prior generation network for deblurring. Extensive experiments demonstrate that BlurDM significantly and consistently enhances existing deblurring methods on four benchmark datasets. The project page is available at https://jin-ting-he.github.io/BlurDM/.

Diffusion models have emerged as state-of-the-art in image synthesis.However, it often suffer from semantic instability and slow iterative denoising. We introduce Latent Alignment Framework (LABridge), a novel Text-Image Latent Alignment Framework via an Ornstein-Uhlenbeck (OU) Process, which explicitly preserves and aligns textual and visual semantics in an aligned latent space. LABridge employs a Text-Image Alignment Encoder (TIAE) to encode text prompts into structured priors that are directly aligned with image latents.