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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.

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Metadaten
Author:Julius Berner, Lorenz Richter, Karen Ullrich
Document Type:In Proceedings
Parent Title (English):NeurIPS 2022 Workshop on Score-Based Methods
Fulltext Url:https://openreview.net/forum?id=jlgs_E-0UdM
Year of first publication:2022
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