Flow Map Denoisers: Traversing the Distortion-Perception Plane for Inverse Problems

Image restoration faces a fundamental tradeoff: methods that minimize error produce blurry reconstructions, while those that maximize perceptual quality yield sharp but less faithful images. Existing approaches either commit to a single operating point on this distortion–perception (DP) frontier or require retraining, auxiliary models, or changes in discretization to access different points. We show that flow map models, a recent extension of flow matching for few-step sampling that learns an average field, implicitly define a one-parameter family of denoisers that continuously spans the DP frontier. The parameter, the lookahead $t$, acts as a knob: varying it traces a smooth path from the MMSE estimator to a perceptually aligned one. For Gaussian targets, we prove that this path recovers the optimal DP frontier exactly; for natural images, we demonstrate empirically that it closely follows the same behavior. Embedded within a Plug-and-Play solver, a single trained flow map matches or exceeds specialized baselines at both ends of the DP spectrum and uniquely traces a continuous curve in between without retraining, paired data, or auxiliary networks. Extensive experiments on CelebA ($128\times 128$) and AFHQ ($256\times 256$) across several linear and nonlinear inverse tasks validate our findings.