Analysis of Flow-based Generative Models

Abstract:
In this talk, we will discuss recent progress on mathematical analysis of flow based generative models, which is a highly successful approach for learning a probability distribution from data and generating further samples.

We will talk about some recent results in convergence analysis of diffusion models and related flow-based methods. In particular, we established convergence of score-based diffusion models applying to any distribution with bounded 2nd moment, relying only on a $L^2$-accurate score estimates, with polynomial dependence on all parameters and no reliance on smoothness or functional inequalities. We will also discuss convergence analysis of flow-based generative models based on tools from optimal transportation, viewing the forward process as a proximal gradient descent under Wasserstein metric.

Bio:
Jianfeng Lu is a Professor of Mathematics, Physics, and Chemistry at Duke University. Before joining Duke University, he obtained his PhD in Applied Mathematics from Princeton University in 2009 and was a Courant Instructor at New York University from 2009 to 2012. He works on mathematical analysis and algorithm development for problems and challenges arising from computational physics, theoretical chemistry, materials science, high-dimensional PDEs, and machine learning. He is a fellow of AMS. His work has been recognized by a Sloan Fellowship, a NSF Career Award, the IMA Prize in Mathematics and its Applications, and the Feng Kang Prize.