Theory for Sampling with Diffusion Models Under Minimal Data Assumptions

AI-generated data, such as images and videos, are typically produced using diffusion models. Generating such data is fundamentally a sampling problem, usually addressed by discretizing a stochastic differential equation. I will present convergence results for samplers used in diffusion models, providing theoretical justification for why the generated images and videos look realistic. In particular, I will present the first polynomial-complexity guarantee that applies without assuming any form of convexity of the target distribution and, time permitting, an improved complexity guarantee whose explicit dependence on the dimension is removed.

Joint work with Sitan Chen, Sinho Chewi, Khashayar Gatmiry, Jerry Li, Yuanzhi Li, and Anru R. Zhang.