Publication

Flower: A Flow-Matching Solver for Inverse Problems

Michaël Unser
2025

Abstract

We introduce Flower, a solver for linear inverse problems. It leverages a pretrained flow model to produce reconstructions that are consistent with the observed measurements. Flower operates through an iterative procedure over three steps: (i) a flow-consistent destination estimation, where the velocity network predicts a denoised target; (ii) a refinement step that projects the estimated destination onto a feasible set defined by the forward operator; and (iii) a timeprogression step that re-projects the refined destination along the flow trajectory. We provide a theoretical analysis that demonstrates how Flower approximates Bayesian posterior sampling, thereby unifying perspectives from plugand-play methods and generative inverse solvers. On the practical side, Flower achieves state-of-the-art reconstruction quality while using nearly identical hyperparameters across various linear inverse problems. Our code is available at https://github.com/mehrsapo/Flower.

Official source

https://infoscience.epfl.ch/entities/publication/27803b33-22ad-413a-99e5-a6b7410a0464

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Michaël Unser
2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/27803b33-22ad-413a-99e5-a6b7410a0464

About this result

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