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

arXiv: https://arxiv.org/abs/2606.19802 · HTML: https://mlsanity.com/paper/2606.19802/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 75 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Flow Map Language Models: One-step Language Modeling via Continuous Denoising](https://mlsanity.com/paper/2602.16813/) (2026)
- [Diffusion models for inverse problems](https://mlsanity.com/paper/2508.01975/) (2025)
- [Test-time scaling of diffusions with flow maps](https://mlsanity.com/paper/2511.22688/) (2025)

## Built on by (most cited first, 2 of 2)

- [Fast and Faithful: Principled Conditional Flow Matching for Inverse Problems](https://mlsanity.com/paper/2609.12953/) (2026)
- [Rethinking Prediction Horizons: Decoupling Model Queries from State Updates in Few-Step MeanFlow](https://mlsanity.com/paper/2610.20071/) (2026)

## Abstract (arXiv)

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× 128) and AFHQ (256× 256) across several linear and nonlinear inverse tasks validate our findings.