An optimal control perspective on diffusion-based generative modeling
- We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs) such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences.
| Author: | Julius Berner, Lorenz Richter, Karen Ullrich |
|---|---|
| Document Type: | In Proceedings |
| Parent Title (English): | Transactions on Machine Learning Research |
| Year of first publication: | 2024 |
| URL: | https://openreview.net/forum?id=oYIjw37pTP |
