Repository: Freie Universität Berlin, Math Department

Improved sampling via learned diffusions

Richter, Lorenz and Berner, Julius and Liu, Guang-Horng (2023) Improved sampling via learned diffusions. Preprint . (Unpublished)

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Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes. In this work, we identify these approaches as special cases of the Schrödinger bridge problem, seeking the most likely stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches.

Item Type:Article
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:3047
Deposited By: Jana Jerosch
Deposited On:18 Jan 2024 11:53
Last Modified:02 Feb 2024 11:41

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