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We introduce and study a class of probabilistic generative models, where thelatent object is a finite-dimensional diffusion process on a finite timeinterval and the observed variable is drawn conditionally on the terminal pointof the diffusion. We make the following contributions:  We provide a unified viewpoint on both sampling and variational inference insuch generative models through the lens of stochastic control.  We quantify the expressiveness of diffusion-based generative models.Specifically, we show that one can efficiently sample from a wide class ofterminal target distributions by choosing the drift of the latent diffusionfrom the class of multilayer feedforward neural nets, with the accuracy ofsampling measured by the Kullback-Leibler divergence to the targetdistribution.  Finally, we present and analyze a scheme for unbiased simulation ofgenerative models with latent diffusions and provide bounds on the variance ofthe resulting estimators. This scheme can be implemented as a deep generativemodel with a random number of layers.

Theoretical guarantees for sampling and inference in generative models with latent diffusions