We are excited to welcome Renyuan Xu, WiSE Gabilan Assistant Professor in the Daniel J. Epstein Department of Industrial and Systems Engineering at the University of Southern California, to the Peter Carr BQE Lecture Series.
Some Mathematical Results on Generative Diffusion Models
Generative diffusion models, which transform noise into new data instances by reversing a Markov diffusion process in time, have become a cornerstone in modern generative models. A key component of these models is to learn the associated Stein's score function. While the practical power of diffusion models has now been widely recognized, the theoretical developments remain far from mature. Notably, it remains unclear whether gradient-based algorithms can learn the score function with a provable accuracy. In this talk, we develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models and the accuracy of score estimation. Our analysis covers both the optimization and the generalization aspects of the learning procedure, which also builds a novel connection to supervised learning and neural tangent kernels.
This is based on joint work with Yinbin Han and Meisam Razaviyayn (USC).
Renyuan Xu is a WiSE Gabilan Assistant Professor in the Daniel J. Epstein Department of Industrial and Systems Engineering at the University of Southern California. From 2019-2021 she was a Hooke Research Fellow in the Mathematical Institute at the University of Oxford, and before that she completed her Ph.D. in 2019 at the University of California, Berkeley in the Department of Industrial Engineering and Operations Research. Her research interests include stochastic analysis, stochastic controls and games, machine learning theory, and mathematical finance. She is also interested in interdisciplinary topics that integrate methodologies in multiple fields along with their applications in addressing high-stake decision-making problems in large-scale systems. She received an NSF CAREER Award in 2024, the SIAM Financial Mathematics and Engineering Early Career Award in 2023, and a JP Morgan AI Faculty Research Award in 2022.