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arXiv · 2509.26287

Flower: A Flow-Matching Solver for Inverse Problems

Mehrsa Pourya·Bassam El Rawas·Michael Unser
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Abstract

We introduce Flower, a solver for linear inverse problems. It leverages a pre-trained 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 time-progression 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 plug-and-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.

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Mehrsa Pourya, Bassam El Rawas, Michael Unser. 2025-09-30. Flower: A Flow-Matching Solver for Inverse Problems. https://arxiv.org/abs/2509.26287

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