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Statistics Seminar - Maxim Raginsky (UIUC): Neural SDEs: Deep Generative Models in the Diffusion Limit

Event Type
Department of Statistics
106B8 Engineering Hall
Sep 15, 2022   4:00 pm  
Originating Calendar
Department of Statistics Event Calendar


Neural SDEs: Deep Generative Models in the Diffusion Limit


In deep generative models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small independent Gaussian perturbation. In this talk, based on joint work with Belinda Tzen, I will discuss the diffusion limit of such models, where we increase the number of layers while sending the step size and the noise variance to zero. I will first provide a unified viewpoint on both sampling and variational inference in such generative models through the lens of stochastic control. Then I will show how we can quantify the expressiveness of diffusion-based generative models. Specifically, I will prove that one can efficiently sample from a wide class of terminal target distributions by choosing the drift of the latent diffusion from the class of multilayer feedforward neural nets, with the accuracy of sampling measured by the Kullback-Leibler divergence to the target distribution. Finally, I will briefly discuss a scheme for unbiased, finite-variance simulation in such models. This scheme can be implemented as a deep generative model with a random number of layers


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