An Optimal Control Perspective on Diffusion-Based Generative Modeling

In May 2024 Lorenz Richter presented his work on diffusion-based generative models at the Machine Learning and Dynamical Systems Seminar of the Alan Turing Institute London.


Abstract:
This seminar will delve into the intersection of generative modeling via Stochastic Differential Equations (SDEs) and three pivotal areas of mathematics: stochastic optimal control, Partial Differential Equations (PDEs), and path space measures. This integration is foundational for both theoretical advancements and practical applications, such as transferring methods across fields or developing innovative algorithms for sampling from unnormalized densities. We introduce a variational framework that employs divergences between path space measures of time-reversed diffusion processes, drawing parallels to the classic Schrödinger bridge problem. This framework enables the use of novel divergence forms like the log-variance divergence, which avoids the pitfalls of the reverse Kullback-Leibler divergence and significantly enhances algorithmic performance across various methodologies.