@inproceedings{BernerRichterUllrich2024, author = {Berner, Julius and Richter, Lorenz and Ullrich, Karen}, title = {An optimal control perspective on diffusion-based generative modeling}, booktitle = {Transactions on Machine Learning Research}, year = {2024}, 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 theory. Further, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences.}, language = {en} }