POST-TRAIN THE MAP YOU SOLVE: DEPLOYMENT-ALIGNED SPECIALIZATION FOR FEW-STEP FLOW SAMPLING

Flow matching trains a continuous velocity field, but few-step sampling deploys a solver- and budget-specific finite map. We post-train that exact map by differentiating a terminal distribution objective through the deployed solver. A shared field–clock repair is followed by tiny solver-specific residual clocks, activated only when held-out target alignment predicts a gain. At 12 field evaluations on a public conditional-flow receiver trained with C²OT (conditional optimal transport), shared repair lowers mean CleanFID10k from 46.824 to 7.704; a 120-parameter residual package reaches 7.334 and is favorable in 10/10 retrainings for each active solver. On the official Scalable Interpolant Transformer (SiT) checkpoint, a frozen finite-stage operator improves Heun and fourth-order Runge–Kutta in every paired 50,000-sample ImageNet Fréchet Inception Distance (FID) evaluation and transfers without target-budget fitting to 8 and 24 field evaluations. B-series analysis and measured error orders trace these gains to tableau-dependent finite-step error. The alignment rule also predicts held-out directions on a second architecture and non-image receivers, while an alternative objective and independent feature representations corroborate the effect. The method keeps one field across solvers and adds no field evaluations; held-out evidence determines which residual clocks are stored.