Discretization and Distribution Learning in Diffusion Models

Explore the mathematical foundations of diffusion models through this 48-minute conference talk that examines discretization techniques and distribution learning approaches. Learn about the literature on discretization of diffusion models, with particular focus on using randomized midpoints for both deterministic and stochastic samplers. Discover how sampling guarantees can reduce distribution learning problems, specifically learning to generate samples, to score matching techniques. Examine how other forms of distribution learning, including parameter estimation and density estimation, can also be reduced to score matching. Understand the practical implications of these theoretical results, including the asymptotic efficiency of DDPM-based parameter estimators and algorithms for Gaussian mixture density estimation. Gain insights into establishing cryptographic hardness results for score estimation and explore the broader mathematical framework that underlies modern diffusion model architectures.