ICSI Seminar: Diffusion Generative Models Beyond Computer Vision: Harnessing Non-Euclidean Data, and Quantifying Knowledge Creation — Prof. Molei Tao

Abstract: As a major powerhouse of generative AI, diffusion models have achieved remarkable success in generating images and videos, which are naturally represented as Euclidean data. Their potential, however, extends far beyond computer vision, reaching into a broad range of scientific and engineering domains. This talk will discuss two research directions that arise in this broader context.

First, Prof. Tao will discuss non-Euclidean diffusion models, including those for discrete data, data on manifolds, data constrained to feasible sets, and data involving multiple such modalities. Just like the Euclidean case, these cases also correspond to important applications, some just emerging, including (vision-) language models, robotic motion planning, molecular engineering, and the design of quantum systems.

Second, he will present an initial step toward understanding how diffusion models benefit specific downstream scientific tasks. Generative AI is presumably not useful if it merely memorizes the training data; but when a diffusion model does not memorize, what kinds of new samples does it generate? This question is relevant not only to privacy and copyright, but also to understanding what new information or knowledge may be produced by generative models. He will make explicit the inductive bias underlying diffusion models, quantifying how they generalize entirely based on the empirical distribution, without invoking any population limit.

Speaker Bio: Prof. Molei Tao is a Professor and Richard Duke Fellow at Georgia Tech, a founding director of the GT AI4Science Center, and currently a visiting professor at the Simons Institute at UC Berkeley. He received his B.S. from Tsinghua University and Ph.D. from Caltech, and previously worked as a Courant Instructor before joining Georgia Tech.

He is the recipient of numerous honors, including the W.P. Carey Ph.D. Prize in Applied Mathematics (2011), NSF CAREER Award (2019), AISTATS Best Paper Award (2020), Cullen-Peck Scholar Award (2022), GT-Emory AI.Humanity Award (2023), SONY Faculty Innovation Award (2024), and Richard Duke Fellowship (2025). Trained as an applied and computational mathematician, his recent research interests include diffusion generative models and sampling, deep learning theory and optimization, and AI4Science.