A Journey Through Diffusions

Abstract

Diffusion processes refer to a class of stochastic processes driven by Brownian motion. They have been widely used in various applications, ranging from engineering to science to finance. In this talk, I will discuss my experiences with diffusion and how this powerful tool has shaped our research programs. I will go over several research projects in the area of control, inference, and machine learning, where we have extensively utilized tools from diffusion processes. In particular, I will present our research on four topics: i) covariance control in which we aim to regulate the uncertainties of a dynamic system; ii) distribution control where we seek to herd population dynamics; iii) Monte Carlo Markov chain sampling for general inference tasks; iv) and diffusion models for generative modeling in machine learning.