February 2024 Diffusion Schrödinger Bridges for Bayesian Computation
Jeremy Heng, Valentin De Bortoli, Arnaud Doucet
Author Affiliations +
Statist. Sci. 39(1): 90-99 (February 2024). DOI: 10.1214/23-STS908


Denoising diffusion models are a novel class of generative models that have recently become extremely popular in machine learning. In this paper, we describe how such ideas can also be used to sample from posterior distributions and, more generally, any target distribution whose density is known up to a normalizing constant. The key idea is to consider a forward “noising” diffusion initialized at the target distribution, which “transports” this latter to a normal distribution for long diffusion times. The time reversal of this process, the “denoising” diffusion, thus “transports” the normal distribution to the target distribution and can be approximated so as to sample from the target. To accelerate simulation, we show how one can introduce and approximate a Schrödinger bridge between these two distributions, that is, a diffusion which transports the normal to the target in finite time.

Funding Statement

A.D. is partially supported by EPSRC Grants EP/R03 4710/1 (CoSinES) and EP/R018561/1 (Bayes4Health).
J.H. was funded by CY Initiative of Excellence (grant “Investissements d’Avenir” ANR-16-IDEX-0008).


Download Citation

Jeremy Heng. Valentin De Bortoli. Arnaud Doucet. "Diffusion Schrödinger Bridges for Bayesian Computation." Statist. Sci. 39 (1) 90 - 99, February 2024. https://doi.org/10.1214/23-STS908


Published: February 2024
First available in Project Euclid: 18 February 2024

MathSciNet: MR4718528
Digital Object Identifier: 10.1214/23-STS908

Keywords: Optimal transport , Schrödinger bridge , score matching , Stochastic differential equation , Time reversal

Rights: Copyright © 2024 Institute of Mathematical Statistics


This article is only available to subscribers.
It is not available for individual sale.

Vol.39 • No. 1 • February 2024
Back to Top