3:00–4:00 pm
Title: Toward Physical Generative Models
Abstract:
Generative models (GMs) are algorithms that take samples from a target probability distribution and return more samples from the same distribution. We will review dynamical versions of such algorithms, variously called score-based diffusions or flow-matching-type generative models. We will interpret these as random dynamical systems, and this allows us to ask some questions about their properties that will enhance our understanding of when and why they work. One question is whether GMs produce ``physical’’ samples or samples close to the support of the true target distribution, even though they make algorithmic errors. To ask a second question, we will consider a lazy generative model, where we apply any random dynamical system to the given samples from the target such that the distribution at a finite time is close to a Gaussian distribution. In principle, we cannot invert this ``noising’’ process to get back target samples, but when can we approximately recover samples from close to the same support?
The first part is joint work with Adriaan de Clercq (UChicago) and the second with Georg Gottwald (U Sydney).