Bridging Stochastic Processes and Generative AI: Mathematical Foundations and Scalable Algorithms for Flow and Diffusion Models

Abstract: Flow and diffusion-based models have transformed modern generative AI by utilizing stochastic processes to represent complex data distributions. In this talk, I will present a unified mathematical framework that connects discrete and continuous diffusion models through Markov processes, leading to new insights into their accuracy and stability. Building on this foundation, I will discuss algorithmic advances for fast, lightweight, and scalable inference, including high-order solvers and inference-time scaling, and outline future directions in physics-informed and scientific generative modeling.