From Diffusion Models to Schrödinger Bridges - When Generative Modeling meets Optimal Transport
Date: Thu, Apr 10, 2025
Location: Online, Zoom
Conference: Kantorovich Initiative Seminar
Subject: Mathematics
Class: Scientific
CRG: Pacific Interdisciplinary Hub on Optimal Transport
Abstract:
Denoising Diffusion models have revolutionized generative modeling. Conceptually, these methods define a transport mechanism from a noise distribution to a data distribution. Recent advancements have extended this framework to define transport maps between arbitrary distributions, significantly expanding the potential for unpaired data translation. However, existing methods often fail to approximate optimal transport maps, which are theoretically known to possess advantageous properties. In this talk, we will show how one can modify current methodologies to compute Schrödinger bridges—an entropy-regularized variant of dynamic optimal transport. We will demonstrate this methodology on a variety of unpaired data translation tasks.