Diffusion Schrödinger Bridge Matching: When Resampling Fails

Teodora Reu, Michael M. Bronstein, Francisco Vargas

Keywords: Diffusion Schrödinger Bridge Matching, Rectified Flows, Marginal Drift, Error Accumulation

TL;DR: DSBM resampling fails to prevent error accumulation, drifts twice as fast as Rectified Flow under constant shifts.

Abstract:

Diffusion Schrodinger Bridge Matching (DSBM) is often argued to resist error accumulation because each forward and backward update resamples from the true marginals. In this paper, we study that claim in a controlled toy model that replaces learned stochastic bridge dynamics with perturbed exact Gaussian optimal transport maps, allowing rigorous tracking of the integrated marginals.

Within this toy setting, we show that resampling alone is not a universal mechanism for robustness. Under constant shift perturbations, both the resampling and no-resampling variants drift linearly, while the resampling variant accumulates error twice as fast because forward and backward biases compound. Under variance-scaling perturbations, the behavior differs qualitatively across variants, showing that stability depends on the perturbation structure rather than on resampling alone.

We complement the theory with experiments using exact OT maps and learned neural regressors. These experiments reproduce the predicted drift phenomena and show additional shape distortion for learned maps. Overall, our results should be interpreted as a toy counterexample to the claim that bidirectional resampling by itself explains robustness to non-additive error.

Submission Number: 59