Piecewise deterministic generative models

Bertazzi Andrea, École Polytechnique

Score based generative models (SGMs) are algorithms that successfully generate realistic data points by learning the score of a perturbed version of the data distribution. In one version of SGMs, the noising part corresponds to the simulation of a diffusion process initialised at the data distribution until it is close to its stationary distribution, which is typically chosen to be standard normal. On the other hand, the denoising map corresponds to the simulation of the time reversed diffusion, for which analytic formulas exist and crucially depend on the score of the (perturbed) data distribution. In this talk, we discuss how to design generative algorithms based on piecewise deterministic Markov processes (PDMPs) instead of diffusions. PDMPs are non-diffusive stochastic processes that combine deterministic motion with random events at Poisson times and have received substantial interest in the context of modelling as well as Markov chain Monte Carlo algorithms. We shall show that, when the noising map is a PDMP, then the denoising map is again a PDMP with dynamics which depend on ratios of perturbed versions of the data distribution. We discuss how to estimate these quantities, obtaining novel generative algorithms based on PDMPs from the MCMC literature.

Area: IS6 - Generative modelling and stochastic mass transport (Giovanni Conforti)

Keywords: Generative models, Piecewise Deterministic Markov processes

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