An optimal control perspective on diffusion-based generative modeling Article Swipe
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· 2022
· Open Access
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· DOI: https://doi.org/10.48550/arxiv.2211.01364
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 can formulate diffusion-based generative modeling as a minimization of the Kullback-Leibler divergence between suitable measures in path space. Finally, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences. We demonstrate that our time-reversed diffusion sampler (DIS) can outperform other diffusion-based sampling approaches on multiple numerical examples.
Related Topics To Compare & Contrast
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2211.01364
- https://arxiv.org/pdf/2211.01364
- OA Status
- green
- Cited By
- 6
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4308163982