An optimal control perspective on diffusion-based generative modeling

arXiv:2211.01364v3 Announce Type: replace
Abstract: 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 …

abstract arxiv control cs.lg differential diffusion equation evolution generative generative modeling generative models hamilton math.oc modeling perspective stat.ml stochastic type