Better Trajectories, Not More: Paired Posterior Correction for Flow-Matching Inverse Problems

We propose *PPC-Flow* (Paired Posterior Correction), a training-free flow-matching solver for linear image inverse problems. The strongest flow-matching solvers re-inject noise and average independent trajectories, which multiplies their cost and gives up the speed advantage of flow priors. We trace their error to two sources, a bias that builds up late in the trajectory and the variance of the re-injected noise. The bias arises because the proximal weight follows a fixed schedule that vanishes near the terminal time, which leaves the pull of the network toward the prior uncorrected in the final steps. Averaging independent trajectories reduces only the variance, and only at the Monte Carlo rate. *PPC-Flow* counters the bias with a posterior velocity correction, which scales up the proximal correction, and suppresses the variance by antithetic pairing of the re-injection noise, both without additional network evaluations. On the CelebA and AFHQ-Cat benchmarks, *PPC-Flow* achieves state-of-the-art PSNR and SSIM among flow-matching solvers while using only 40% of the NFE budget. Code and video are available at https://anonymous.4open.science/r/ppc-flow-C40F.