{"ID":2862808,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.26287","arxiv_id":"2509.26287","title":"Flower: A Flow-Matching Solver for Inverse Problems","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.","short_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 predic...","url_abs":"https://arxiv.org/abs/2509.26287","url_pdf":"https://arxiv.org/pdf/2509.26287v2","authors":"[\"Mehrsa Pourya\",\"Bassam El Rawas\",\"Michael Unser\"]","published":"2025-09-30T14:07:10Z","proceeding":"cs.CV","tasks":"[\"cs.CV\",\"cs.LG\"]","methods":"[]","has_code":false,"code_links":[{"ID":608946,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2862808,"paper_url":"https://arxiv.org/abs/2509.26287","paper_title":"Flower: A Flow-Matching Solver for Inverse Problems","repo_url":"https://github.com/mehrsapo/Flower","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}