14:00 – 15:00 – Martin Wainwright (MIT)
Title:The Information Geometry of Diffusion Sampling
Abstract: Sampling from a high-dimensional distribution is a core challenge spanning statistics, operations research, applied mathematics and computer science. Diffusion-based methods have led to dramatic advances: in generative AI, they produce strikingly realistic images, video, and text, and they are finding growing use in areas including biology, drug design, materials science, and robotics. In this talk, we introduce a unified way of analyzing the performance of both continuous diffusion samplers (based on Gaussian noise), and discrete analogues. We introduce information-theoretic quantities that control the Kullback–Leibler divergence of a given sampler. They adapt naturally to low dimensional structure in the underlying distribution, and can be substantially smaller than what ambient dimension alone would suggest. Moreover, these path-based measures can be estimated from data, providing a way to calibrate and improve the performance of diffusion samplers.