Theory for Diffusion Models

I will describe recent progress on providing rigorous convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL⋅E 2. In the first part of the talk, I will show that such SGMs can efficiently sample from essentially any realistic data distribution, even ones which are highly non-log-concave. In the second part of the talk, I will show how to extend these guarantees to deterministic samplers based on discretizing the so-called probability flow ODE, which ultimately leads to better dependence on the dimension. All of these results assume access to an oracle for score estimation; time permitting, at the end I will briefly touch upon how to provably implement this oracle for interesting classes of distributions like Gaussian mixtures.

Based on the following works: arxiv.org/abs/2209.11215, arxiv.org/abs/2303.03384, arxiv.org/abs/2305.11798, arxiv.org/abs/2307.01178