SILO: Theory for Diffusion Models

In this talk I will survey our recent efforts to develop a rigorous theory for understanding diffusion generative modeling. The first part will cover discretization analyses that prove that diffusion models can approximately sample from arbitrary probability distributions provided one can have a sufficiently accurate estimate for the score function. The second part will cover new algorithms for score estimation that, in conjunction with the results in the first part, imply new bounds for learning Gaussian mixture models. Time permitting, the third part will then use the lens of mixture models to shed light on two intriguing empirical phenomena of diffusion models: the behavior of diffusion models under guidance, and the emergence of features in narrow windows of time during the generation process.

Sitan Chen is an Assistant Professor of Computer Science at Harvard University, where he is a member of the Theory of Computation, the ML Foundations group, and the Harvard Quantum Initiative. Previously, he was an NSF math postdoc at UC Berkeley, after completing his PhD in EECS at MIT in 2021. His research centers around developing rigorous guarantees for fundamental algorithmic problems in machine learning and quantum information.