Diffusion Schrödinger Bridge paper solves entropy-regularized optimal transport to speed up generative modeling

skoularidou · x · 2026-09-29

Arnaud Doucet reshares his team's 2021 paper Diffusion Schrödinger Bridge with Applications to Score-Based Generative Modeling (arXiv:2106.01357).

• Introduces DSB, an approximation of the Iterative Proportional Fitting (IPF) procedure for solving the Schrödinger Bridge problem — an entropy-regularized optimal transport problem on path spaces
• Unlike score-based models, which require running the forward noising SDE long enough to reach a near-Gaussian distribution, DSB yields diffusions that generate samples from the data distribution in finite time
• The first DSB iteration recovers Song et al. (2021); subsequent iterations reduce the discrepancy between the forward/backward SDE terminal marginals and the prior/data distributions
• Beyond generative modeling, DSB provides a broadly applicable tool for computational optimal transport in high dimensions

Authors: Valentin De Bortoli, James Thornton, Jeremy Heng, Arnaud Doucet.

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