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[2509.26287] Flower: A Flow-Matching Solver for Inverse Problems
Summary
The paper introduces Flower, a novel solver for linear inverse problems that utilizes a pre-trained flow model to enhance reconstruction quality through an iterative three-step process.
Why It Matters
Flower represents a significant advancement in solving linear inverse problems, integrating concepts from Bayesian sampling and generative models. Its ability to achieve state-of-the-art results with consistent hyperparameters across various applications makes it a valuable tool for researchers and practitioners in computer vision and machine learning.
Key Takeaways
- Flower employs a three-step iterative process for effective reconstruction.
- It leverages pre-trained flow models to enhance the accuracy of reconstructions.
- The method approximates Bayesian posterior sampling, bridging different approaches in inverse problem-solving.
- Flower achieves high-quality results while maintaining consistent hyperparameters across diverse problems.
- The code for Flower is publicly available, promoting accessibility and further research.
Computer Science > Computer Vision and Pattern Recognition arXiv:2509.26287 (cs) [Submitted on 30 Sep 2025 (v1), last revised 22 Feb 2026 (this version, v2)] Title:Flower: A Flow-Matching Solver for Inverse Problems Authors:Mehrsa Pourya, Bassam El Rawas, Michael Unser View a PDF of the paper titled Flower: A Flow-Matching Solver for Inverse Problems, by Mehrsa Pourya and 2 other authors View PDF HTML (experimental) 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 this https URL. Subjects: Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG) Cite as: arXiv:2509.26287...
