BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Flower: A Flow-Matching Solver for Inverse Problems

M. Pourya, B. El Rawas, M. Unser

Proceedings of the Fourteenth International Conference on Learning Representations (ICLR'26), Rio de Janeiro, Federative Republic of Brazil, April 23-27, 2026, 26 p.

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 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. 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/pourya2601.html,
AUTHOR="Pourya, M. and El Rawas, B. and Unser, M.",
TITLE="{F}lower: A Flow-Matching Solver for Inverse Problems",
BOOKTITLE="Proceedings of the Fourteenth International Conference on
	Learning Representations ({ICLR'26})",
YEAR="2026",
editor="",
volume="",
series="",
pages="",
address="Rio de Janeiro, Federative Republic of Brazil",
month="April 23-27,",
organization="",
publisher="",
note="")
© 2026 The Authors. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from The Authors. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.