Stochastic Interpolants: A Unifying Framework for Flows and Diffusions - Lecture

Explore a unifying framework for flows and diffusions in generative models through this comprehensive lecture on stochastic interpolants. Delve into the extension of the Albergo & Vanden-Eijnden (2023) framework, which bridges arbitrary probability density functions using continuous-time stochastic processes. Examine the mathematical foundations, including transport equations and Fokker-Planck equations, that govern these interpolants. Discover how this approach leads to both deterministic and stochastic generative models with adjustable noise levels. Investigate the characterization of drift coefficients as minimizers of quadratic objective functions, and understand their impact on likelihood control. Compare deterministic and stochastic dynamics in generative models, exploring the additional requirements for deterministic approaches. Learn about estimators for likelihood and cross-entropy, connections to other stochastic bridges, and the relationship with Schrödinger bridges. Follow along as the speaker covers problem setup, interpolant design, different couplings, multimarginal interpolants, and practical applications, concluding with a Q&A session.

- Intro
- Problem setup
- Stochastic interpolants
- The interpolant score
- Designing different interpolants
- Designing different couplings
- Multimarginal interpolants
- Applications
- Q+A