相关论文: The Effect of Stochasticity in Score-Based Diffusi…

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…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Many normalizing flow architectures impose regularity constraints, yet their distributional approximation properties are not fully characterized. We study the expressivity of bi-Lipschitz normalizing flows through the lens of score-based…

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE…

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…

Diffusion-based generative processes, formulated as differential equation solving, frequently balance computational speed with sample quality. Our theoretical investigation of ODE- and SDE-based solvers reveals complementary weaknesses: ODE…

Recently, diffusion probabilistic models (DPMs) have achieved promising results in diverse generative tasks. A typical DPM framework includes a forward process that gradually diffuses the data distribution and a reverse process that…

We derive a deterministic, non-asymptotic upper bound on the Kullback-Leibler (KL) divergence of the flow-matching distribution approximation. In particular, if the $L_2$ flow-matching loss is bounded by $\epsilon^2 > 0$, then the KL…

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…

Diffusion models generate high-dimensional data with remarkable quality, yet how their training efficiently learns the score function, bypassing the curse of dimensionality when data is supported on low-dimensional manifolds, remains…

Unpaired image-to-image translation involves learning mappings between source domain and target domain in the absence of aligned or corresponding samples. Score based diffusion models have demonstrated state-of-the-art performance in…

We consider the problem of parameter estimation for a class of continuous-time state space models. In particular, we explore the case of a partially observed diffusion, with data also arriving according to a diffusion process. Based upon a…

Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved…

Score-based generative models have excellent performance in terms of generation quality and likelihood. They model the data distribution by matching a parameterized score network with first-order data score functions. The score network can…

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…

Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…

We develop an analytically tractable single-step diffusion model based on a linear denoiser and present an explicit formula for the Kullback-Leibler divergence between the generated and sampling distribution, taken to be isotropic Gaussian,…

We study a worst-case approach to measure the sensitivity to model misspecification in the performance analysis of stochastic systems. The situation of interest is when only minimal parametric information is available on the form of the…

Schr\"{o}dinger bridge can be viewed as a continuous-time stochastic control problem where the goal is to find an optimally controlled diffusion process whose terminal distribution coincides with a pre-specified target distribution. We…

Decision-focused learning (DFL) integrates predictive modeling and optimization by training predictors to optimize the downstream decision target rather than merely minimizing prediction error. To date, existing DFL methods typically rely…