Reflected Schr\"odinger Bridge Matching

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.