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Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…

Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…

Diffusion language models (DLMs) promise parallel, order-agnostic generation, but on standard benchmarks they have historically lagged behind autoregressive models in sample quality and diversity. Recent continuous flow and diffusion…

Diffusion model deployment has been suffering from high energy consumption and inference latency despite its superior performance in visual generation tasks. Dynamic voltage and frequency scaling (DVFS) offers a promising solution to…

In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…

Self-correction is an effective technique for maintaining parallel sampling in discrete diffusion models with minimal performance degradation. Prior work has explored self-correction at inference time or during post-training; however, such…

Diffusion models, such as Stable Diffusion, have shown incredible performance on text-to-image generation. Since text-to-image generation often requires models to generate visual concepts with fine-grained details and attributes specified…

We present DiffusionBERT, a new generative masked language model based on discrete diffusion models. Diffusion models and many pre-trained language models have a shared training objective, i.e., denoising, making it possible to combine the…

Guidance provides a simple and effective framework for posterior sampling by steering the generation process towards the desired distribution. When modeling discrete data, existing approaches mostly focus on guidance with the first-order…

Transfer Learning aims to optimally aggregate samples from a target distribution, with related samples from a so-called source distribution to improve target risk. Multiple procedures have been proposed over the last two decades to address…

We identify and analyze a surprising phenomenon of Latent Diffusion Models (LDMs) where the final steps of the diffusion can degrade sample quality. In contrast to conventional arguments that justify early stopping for numerical stability,…

Diffusion models have achieved state-of-the-art performance in generating many different kinds of data, including images, text, and videos. Despite their success, there has been limited research on how the underlying diffusion process and…

Diffusion models have marked a significant breakthrough in the synthesis of semantically coherent images. However, their extensive noise estimation networks and the iterative generation process limit their wider application, particularly on…

In this paper, we use tools from rate-distortion theory to establish new upper bounds on the generalization error of statistical distributed learning algorithms. Specifically, there are $K$ clients whose individually chosen models are…

Autoregressive (AR) models remain the standard for natural language generation but still suffer from high latency due to strictly sequential decoding. Recent diffusion-inspired approaches, such as LlaDA and Dream, mitigate this by…

The growing sophistication of synthetic image and deepfake generation models has turned source attribution and authenticity verification into a critical challenge for modern computer vision systems. Recent studies suggest that diffusion…

We are interested in the kernel of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step $h>0$ in the limit as $h\to0$. We consider both semidiscrete…

In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

Diffusion models have achieved significant progress in image generation. The pre-trained Stable Diffusion (SD) models are helpful for image deblurring by providing clear image priors. However, directly using a blurry image or pre-deblurred…