# Diffusion Schr\\"odinger Bridge Matching

Source: [Diffusion Schr\\"odinger Bridge Matching](<https://www.sota2.com/research/paper/68fa717a1e209131cea5180c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T02:07:38.985Z

Authors: Yuyang Shi, Valentin De Bortoli, Andrew Campbell, Arnaud Doucet

Published: 2023-03-29T16:59:22.000Z

## Abstract

Solving transport problems, i.e. finding a map transporting one given distribution to another, has numerous applications in machine learning. Novel mass transport methods motivated by generative modeling have recently been proposed, e.g. Denoising Diffusion Models (DDMs) and Flow Matching Models (FMMs) implement such a transport through a Stochastic Differential Equation (SDE) or an Ordinary Differential Equation (ODE). However, while it is desirable in many applications to approximate the deterministic dynamic Optimal Transport (OT) map which admits attractive properties, DDMs and FMMs are not guaranteed to provide transports close to the OT map. In contrast, Schr\\"odinger bridges (SBs) compute stochastic dynamic mappings which recover entropy-regularized versions of OT. Unfortunately, existing numerical methods approximating SBs either scale poorly with dimension or accumulate errors across iterations. In this work, we introduce Iterative Markovian Fitting (IMF), a new methodology for solving SB problems, and Diffusion Schr\\"odinger Bridge Matching (DSBM), a novel numerical algorithm for computing IMF iterates. DSBM significantly improves over previous SB numerics and recovers as special/limiting cases various recent transport methods. We demonstrate the performance of DSBM on a variety of problems.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Intermediate distribution restoration on Single-cell data (intermediate time points ti for i in {1, 2, 3})](<https://www.sota2.com/research/sota/intermediate-distribution-restoration-on-single-cell-data-intermediate-time-points-ti-for-i-in-1-2-3.md>): Intermediate distribution restoration; Single-cell data (intermediate time points ti for i in {1, 2, 3}); W1 Score: 1.775.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2303.16852>)

[PDF](<https://arxiv.org/pdf/2303.16852.pdf>)