TY - CHAP A1 - Berner, Julius A1 - Richter, Lorenz A1 - Ullrich, Karen T1 - An optimal control perspective on diffusion-based generative modeling T2 - NeurIPS 2022 Workshop on Score-Based Methods N2 - 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. Y1 - 2022 ER -