Reflected Schr"odinger Bridge Matching
Marcus Häggbom, Viktor Nilsson, Pierre Nyquist, Joakim andén
cs.LG, stat.ML
Submitted: 2026-07-03
Code: https://github.com/viktor765/rsbm
License: http://creativecommons.org/licenses/by/4.0/
The gist: Recent advances in generative modeling have enabled the efficient computation of Schr"odinger bridges (SB) in high-dimensional settings by leveraging partially simulation-free training methods
Terminology
Abstract
Recent advances in generative modeling have enabled the efficient computation of Schr"odinger bridges (SB) in high-dimensional settings by leveraging partially simulation-free training methods inspired by flow matching. However, these have not covered SBs with reflecting dynamics, a useful model choice with built-in guarantees that generated samples stay in the data domain. Existing alternatives for reflected SBs instead rely on more complex training based on forward--backward SDE theory, requiring expensive higher-order derivatives and sampling entire paths during training. In this article, we introduce a partially simulation-free framework that allows reflected SBs to be trained similarly to flow matching, using a new sampling method and regression target. We demonstrate our results by coupling pairs of well-known high-dimensional image datasets. Using reflected dynamics incurs negligible additional wall-clock time during both training and inference while maintaining or slightly improving generative performance.
Sources
- Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
- Score matching for bridges without learning time-reversals
- The Pedestrian's Guide to Local Time
- Classifier-Free Diffusion Guidance
- Adam: A Method for Stochastic Optimization
- Rectified Flow: A Marginal Preserving Approach to Optimal Transport
- Large deviations for scaled families of Schr\"odinger bridges with reflection
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