Abstract: Generative modeling represents one of the most striking examples of the successes of modern machine learning. In generative modeling, one seeks to artificially generate new data that belongs to given input class. For instance, generating new faces from a database of celebrity faces. Mathematically, this can be posed as finding a map that pushes a simple concrete probability distribution, such as a standard Gaussian, to a complicated abstract distribution that is only known through examples.

Currently, one of the most popular paradigms in generative modeling is diffusion modeling, where the map is constructed by reversing the flow of a diffusion equation applied to the example set. The standard approach in the literature focuses on flowing along a Fokker-Planck equation (i.e. a heat equation with a drift term) and requires stochasticity in the backwards flow to prove convergence rates. In this talk, I will discuss some advantages of flowing along a more general class of diffusion equations and prove convergence rates when the backwards flow is deterministic.

Contact: Selim Esedoglu.