An optimal control perspective on diffusion-based generative modeling

Understand

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.