Generative Modeling with Diffusion and Stochastic Interpolants

Generative Modeling with Diffusion and Stochastic Interpolants  brings together tools, and methods from probability theory, stochastic processes, differential equations, and machine learning, combined into a practical mathematical toolkit for turning noise into realistic data. Its impact spans a wide range of domains: in imaging, it enables high-fidelity synthesis and editing; in the sciences, it supports simulation and inverse problems; and in audio and language, it provides flexible, controllable generation.

This course is designed to be foundational and focuses on building the mathematics needed to understand and analyze these models. It assumes comfort with calculus, linear algebra, and basic probability, and develops MCMC sampling, stochastic differential equations, and the Fokker–Planck and probability-flow formalisms that govern evolving densities. The course then connects these tools to score-based learning, denoising objectives, and sampling algorithms, supported throughout by concrete computational examples.