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

• URL: http://arxiv.org/abs/2606.19802v1
• Date: Thu, 18 Jun 2026 05:15:43 GMT
• Title: Flow Map Denoisers: Traversing the Distortion-Perception Plane for Inverse Problems
• Abstract summary: 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.<n>We show that flow map models implicitly define a one- parameter family of denoisers that continuously spans the distortion perception frontier.<n>Within a Plug-and-Play solver, the same mechanism extends to general inverse problems, where it controls a tradeoff between perceptual alignment and data consistency.
• Score: 48.501415601682815
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 paired-data supervision, auxiliary models, or hyperparameter tuning of the sampler 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 lookahead parameter t acts as a control knob between the MMSE and perceptual regimes. For Gaussian targets, we prove that varying t exactly recovers the optimal DP frontier; for natural images, we observe similar behavior empirically. Within a Plug-and-Play solver, the same mechanism extends to general inverse problems, where it controls a tradeoff between perceptual alignment and data consistency. Despite the lack of exact optimality guarantees in this setting, a single trained flow map spans the DP tradeoff, matching or exceeding specialized baselines at both extremes. Extensive experiments on CelebA ($128\times 128$) and AFHQ ($256\times 256$) across several linear and nonlinear inverse tasks validate our findings.

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