תיקון CondOT: סימולציה דו-צדדית סופית במישורי זרם גאוסיאני

תקציר מקורי באנגליתarXiv:2609.39488v1 Announce Type: new Abstract: Flow matching generates samples by gradually transforming noise into data. In practice, using a finite number of sampling steps introduces a numerical error that depends on the chosen schedule. We study this dependence for Gaussian targets and the explicit midpoint sampling method, using the exact flow field. We measure sampling error by the squared Wasserstein distance between the target distribution and the final distribution produced by the midpoint sampler. We show that the standard conditional optimal transport (CondOT) schedule cancels the leading midpoint error and improves the general convergence bound, even when the sampling steps are unequally spaced. On a uniform grid of $S$ sampling steps, we fix the signal schedule at $\alpha_t=t