Improved sampling via learned diffusions

Published: 16 Jan 2024, Last Modified: 11 Feb 2024ICLR 2024 posterEveryoneRevisionsBibTeX
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Keywords: Schrödinger bridge, sampling from densities, stochastic optimal control, diffusion-based generative modeling
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
TL;DR: We propose a unifying framework to improve diffusion-based samplers.
Abstract: 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, and propose the perspective from measures on path space as a unifying framework. The optimal controls of such entropy-constrained optimal transport problems can then be described by systems of partial differential equations and corresponding backward stochastic differential equations. Building on these optimality conditions and exploiting the path measure perspective, we obtain variational formulations of the respective approaches and recover the objectives which can be approached via gradient descent. Our formulations allow to introduce losses different from the typically employed reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called $\textit{log-variance loss}$, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 6227
Loading