Learning to Match Distributions: Optimal Transport, Flow Matching & Applications
Fall 2026 · New York University Romain Lopez
Time & location TBD
This seminar course explores how to match and transform probability distributions for machine learning applications. The course begins with a few lectures on optimal transport and flow matching, and transitions into a reading group covering contemporary methods and applications across scientific domains.
Prerequisites & requirements.
The class is open to graduate students with a background in machine learning who have taken a course in probability and statistics at the level of
Fernandez-Granda (2024)
or equivalent. Familiarity with convex optimization is helpful but not required.
Students will present and review papers throughout the semester, and complete a semester-long research project.
Part I — Mathematical Foundations
Tentative list of topics covered:
Comparing distributions: divergences, MMD & kernel methods.f-divergences, kernel mean embeddings, maximum mean discrepancy, two-sample testing.