Diffusion Schrödinger Bridge Matching: When Resampling Fails

Iterative algorithms, such as Rectified Flows and Diffusion Schrödinger Bridge Matching (DSBM), have become central to generative modeling. While Rectified Flows are known to accumulate error through marginal drift, DSBM is frequently claimed to mitigate this via bidirectional resampling from true marginals. However, this robustness claim lacks rigorous proof. We introduce two tractable failure modes where theoretical analysis is feasible: constant shift perturbations, under which all methods, including DSBM, exhibit linear marginal drift, with DSBM accumulating error twice as fast as unidirectional methods; and variance scaling perturbations, under which non-resampling methods diverge unboundedly while DSBM stabilizes at diverge unnboundedly (when scaling factors satisfy $\epsilon_f \epsilon_b < 1$). We provide both theoretical analysis and empirical validation using exact OT maps and learned neural networks. Our results demonstrate that resampling alone cannot prevent systematic error accumulation, and can even accelerate it under certain perturbations. These findings indicate that practitioners should monitor marginal quality across iterations and consider early stopping or hybrid approaches when using DSBM-like methods.