CPSC 7430: Topics in flow-based generative modeling and optimal transport

Course Description: Generative modeling has had a major impact across many scientific disciplines in recent years. A driving force has been the development of scalable algorithms that transport, or “flow,” simple reference distributions into complex data distributions. This course explores the mathematical foundations of generative models through the lens of flow-based transport, emphasizing how deterministic and stochastic dynamics can be used to transform probability distributions. Topics include flow matching, stochastic interpolants, diffusion models, optimal transport maps, Schrödinger bridges, and extensions to approximate inference, temporal data, and data on Riemannian manifolds. Students will implement many of these methods while studying statistical questions such as sample complexity and convergence rates, as well as optimization guarantees where available.

Prerequisites: Advanced Probability (S&DS 400 / S&DS 600 / MATH 330), Optimization (S&DS 431 / S&DS 631, or S&DS 432 / S&DS 632), Stochastic Processes (S&DS 351 / S&DS 551), and general mathematical maturity. Prior exposure to neural networks, optimal transport, or generative modeling is not required. Enrollment is limited and requires the instructor’s permission.

Instructor: Aram-Alexandre Pooladian
Time: 9:25am - 11:25am
Location: TBD
Office hours: TBD