Related papers: Lipschitz Singularities in Diffusion Models

Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we…

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

Diffusion models have made rapid progress in generating high-quality samples across various domains. However, a theoretical understanding of the Lipschitz continuity and second momentum properties of the diffusion process is still lacking.…

Personalizing text-to-image diffusion models involves integrating novel visual concepts from a small set of reference images while retaining the model's original generative capabilities. However, this process often leads to overfitting,…

We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed…

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…

Diffusion models (DMs) are a powerful generative framework that have attracted significant attention in recent years. However, the high computational cost of training DMs limits their practical applications. In this paper, we start with a…

Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…

Diffusion models (DMs) have been adopted across diverse fields with its remarkable abilities in capturing intricate data distributions. In this paper, we propose a Fast Diffusion Model (FDM) to significantly speed up DMs from a stochastic…

Adapter-based methods are commonly used to enhance model performance with minimal additional complexity, especially in video editing tasks that require frame-to-frame consistency. By inserting small, learnable modules into pretrained…

Most diffusion models assume that the reverse process adheres to a Gaussian distribution. However, this approximation has not been rigorously validated, especially at singularities, where t=0 and t=1. Improperly dealing with such…

We prove existence and uniqueness of solutions to a class of stochastic semilinear evolution equations with a monotone nonlinear drift term and multiplicative noise, considerably extending corresponding results obtained in previous work of…

In control theory, typically a nominal model is assumed based on which an optimal control is designed and then applied to an actual (true) system. This gives rise to the problem of performance loss due to the mismatch between the true model…

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…

We study a class of semilinear diffusion equations on infinite, connected, weighted graphs, focusing on two types of nonlinearities: monotone decreasing and Lipschitz continuous. Under minimal structural assumptions on the graph, we…

The increased model capacity of Diffusion Transformers (DiTs) and the demand for generating higher resolutions of images and videos have led to a significant rise in inference latency, impacting real-time performance adversely. While prior…

The classical result by It\^o on the existence of strong solutions of stochastic differential equations (SDEs) with Lipschitz coefficients can be extended to the case where the drift is only measurable and bounded. These generalizations are…

While diffusion models excel at generating continuous data such as images, adapting them to discrete tasks has relied on indirect approaches that either operate in continuous embedding spaces or use token masking mechanisms, both of which…

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…

Standard Latent Diffusion Models rely on a complex, three-part architecture consisting of a separate encoder, decoder, and diffusion network, which are trained in multiple stages. This modular design is computationally inefficient, leads to…