Flow Map Denoisers Balance Image Quality and Fidelity in Inverse Problems

Image restoration tasks inherently involve a fundamental compromise: methods designed to minimize reconstruction error often result in blurry images, whereas approaches prioritizing perceptual quality tend to produce sharper but potentially less faithful results. Current solutions typically commit to a specific point on this distortion-perception (DP) frontier or demand complex setups like paired-data supervision, auxiliary models, or extensive hyperparameter tuning for sampling. This research introduces flow map models, an extension of flow matching for few-step sampling, as a solution. These models implicitly define a continuous family of denoisers controlled by a single parameter. This "lookahead" parameter, denoted as 't', acts as a simple control knob, allowing users to smoothly navigate between the mean squared error (MMSE) regime, which prioritizes fidelity, and the perceptual regime, which emphasizes sharpness. For Gaussian targets, the study theoretically proves that varying 't' precisely recovers the optimal DP frontier. Empirical observations on natural images show similar behavior. When integrated into a Plug-and-Play solver, this mechanism extends to general inverse problems, controlling the balance between perceptual alignment and data consistency. Despite lacking exact optimality guarantees in this broader context, a single trained flow map effectively spans the DP tradeoff, matching or surpassing specialized baselines at both extremes. Extensive experiments on CelebA and AFHQ datasets across various linear and nonlinear inverse tasks validate these findings.