Related papers: How Discrete and Continuous Diffusion Meet: Compre…

We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…

Denoising diffusion probabilistic models have transformed image generation with their impressive fidelity and diversity. We show that they also excel in estimating optical flow and monocular depth, surprisingly, without task-specific…

This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…

Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…

Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…

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…

Discrete flow models (DFMs) have been proposed to learn the data distribution on finite state space, offering a flexible framework as an alternative to discrete diffusion models. A line of recent work has studied samplers for discrete…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…

In this paper, we study the problem of computing the effective diffusivity for particles moving in chaotic flows. Instead of solving a convection-diffusion type cell problem in the Eulerian formulation (arising from homogenization theory…

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…

Generative modeling of non-negative, discrete data, such as symbolic music, remains challenging due to two persistent limitations in existing methods. Firstly, many approaches rely on modeling continuous embeddings, which is suboptimal for…

This paper introduces Discrete Markov Probabilistic Models (DMPMs), a novel discrete diffusion algorithm for discrete data generation. The algorithm operates in discrete bit space, where the noising process is a continuous-time Markov chain…

Diffusion or score-based models recently showed high performance in image generation. They rely on a forward and a backward stochastic differential equations (SDE). The sampling of a data distribution is achieved by numerically solving the…

Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…

We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an…

This article develops a methodology allowing application of the complete machinery of particle-based inference methods upon the class of continuous-discrete State Space Models (CD-SSMs). Such models correspond to a latent continuous-time…

We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead,…

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…

One of the main contributions of this paper is to illustrate how large deviation theory can be used to determine the equilibrium distribution of a basic droplet model that underlies a number of important models in material science and…