Divergence is Uncertainty: A Closed-Form Posterior Covariance for Flow Matching

arXiv:2605.00941v1 Announce Type: new Abstract: Flow matching has become a leading framework for generative modeling, but quantifying the uncertainty of its samples remains an open problem. Existing approaches retrain the model with auxiliary variance heads, maintain costly ensembles, or propagate approximate covariance through many integration steps, trading off training cost, inference cost, or accuracy. We show that none of these trade-offs is necessary. We prove that, for any pre-trained flo...