Course Info

This is a graduate topics class on theoretical aspects of modern machine learning. This iteration will focus on recent developments in diffusion generative modeling. Diffusion and flow-based models are now the dominant approach to generative modeling across a wide range of data modalities, powering state-of-the-art systems for images, audio, video, and beyond. Alongside this empirical success has come a surge of interest in developing the mathematical foundations that undergird these methods, out of which has grown a rich exchange of ideas between the practice of generative modeling on the one hand, and physics, statistics, and theoretical computer science on the other.

The course is an attempt to distill some of these ideas. The course will explore foundational aspects (Itô processes, discretization analysis, connections to stochastic optimal control and stochastic localization, and the complexity of score estimation) as well as empirical aspects for which the associated theory is still nascent (consistency models, guided generation, the mystery of generalization, and diffusion language models).

The goal is that by the end of the course, students will be sufficiently up to date with the modern literature on the science and theory of diffusion models that they are ready to engage in original research.