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

2026-06-18

AI Summary

This work addresses the fundamental trade-off between distortion and perceptual quality in image restoration, which traditional methods struggle to balance flexibly within a single model. The authors propose a flow map–based denoiser parameterized by a single lookahead parameter \( t \), enabling continuous traversal along the distortion–perception frontier. Embedded within a Plug-and-Play framework, this approach solves diverse inverse problems without requiring additional supervision, auxiliary models, or hyperparameter tuning. Notably, the method reveals that flow-based models implicitly define a continuous family of solutions spanning the entire frontier, achievable with just one trained model. Experiments on CelebA (128×128) and AFHQ (256×256) demonstrate that the proposed model matches or surpasses specialized baselines designed exclusively for either distortion minimization or perceptual quality across various linear and nonlinear inverse problems.

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.

Problem

• distortion-perception tradeoff
• image restoration
• inverse problems
• perceptual quality
• denoising

Innovation

• flow map denoiser
• distortion-perception tradeoff
• inverse problems
• perceptual quality
• Plug-and-Play