An Optimal Control Perspective on Diffusion-Based Generative Modeling

Explore an in-depth lecture on the connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs). Delve into the derivation of a Hamilton-Jacobi-Bellman equation governing the evolution of log-densities of SDE marginals. Discover how this perspective allows for the transfer of methods from optimal control theory to generative modeling. Learn about the evidence lower bound as a consequence of the verification theorem from control theory. Examine a novel diffusion-based method for sampling from unnormalized densities, applicable to statistics and computational sciences. Follow along as the speaker covers topics such as SDE-based modeling, the Fokker-Planck equation, score matching, and compares Time Reversed Diffusion Sampler (DIS) with Path Integral Sampler (PIS). Engage with the Q&A session at the end to further understand this optimal control perspective on diffusion-based generative modeling.

- Intro
- The Task of Generative Modeling
- Overview of the Talk
- SDE-based Modeling
- The Fokker-Planck Equation
- Deriving the ELBO + Verification Theorem
- Denoting Score Matching
- Summary
- Time Reversed Diffusion Sampler DIS
- Path Integral Sampler PIS
- DIS vs. PIS
- Q+A