Changxiao Cai
University of Michigan
3:30 PM
154 Hurley Hall
Towards Statistical and Algorithmic Foundations of Diffusion Models
Score-based diffusion models have emerged as a foundational paradigm for modern generative modeling, achieving remarkable success across diverse applications from image synthesis to scientific computing. Despite their empirical prominence, fundamental questions about their theoretical foundations remain: How efficient can diffusion samplers be? What are the fundamental statistical limits of these samplers? In this talk, I will present recent theoretical advances that address both the computational and statistical frontiers of diffusion models. First, I will introduce a novel accelerated stochastic sampler that provably reduces iteration complexity under minimal assumptions, offering sampling speedups without sacrificing statistical optimality. Second, I will present the first comprehensive end-to-end analysis for deterministic ODE-based samplers, establishing (near-)minimax optimal statistical guarantees under mild assumptions on the target distribution. Together, these results provide a rigorous mathematical foundation that narrows the gap between the practical success and theoretical understanding of diffusion models. This is joint work with Gen Li.
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