Reflected Schrödinger Bridge Matching

2026-07-03

AI Summary

Existing reflected Schrödinger bridge methods incur substantial computational costs due to their reliance on high-order derivatives and full-path sampling. This work proposes a lightweight, partially simulation-free training framework that reformulates the problem in a flow-matching-like setting. By integrating reflected stochastic differential equations, a novel sampling strategy, and a tailored regression objective, the approach eliminates the need for both path sampling and high-order differentiation while rigorously enforcing sample confinement within the data domain. Evaluated on high-dimensional image-to-image translation tasks, the method achieves generation performance on par with or superior to baseline approaches, with negligible additional overhead in both training and inference.

Abstract

Recent advances in generative modeling have enabled the efficient computation of Schrödinger 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.

Problem

• reflected Schrödinger bridge
• generative modeling
• flow matching
• stochastic differential equations
• simulation-free training

Innovation

• reflected Schrödinger bridge
• flow matching
• simulation-free training
• generative modeling
• stochastic differential equations