用预训练流模型解决线性逆问题，重建效果领先且参数通用。
Flower: A Flow-Matching Solver for Inverse Problems
- 基于流模型迭代优化，三步流程融合去噪与约束投影。
- 在多种逆问题上达到当前最优重建质量，超参几乎不变。
- 适合图像重建、医学成像等需要高质量逆解的场景。
我们提出 Flower，一种用于线性逆问题的求解器。它利用预训练的流模型生成与观测数据一致的重建结果。Flower 通过三个步骤的迭代过程实现：(i) 流一致性目标估计，速度网络预测去噪后的目标；(ii) 修正步骤，将估计目标投影到由前向算子定义的可行集上；(iii) 时间推进步骤，沿流轨迹重新投影修正后的目标。我们提供了理论分析，证明 Flower 可近似贝叶斯后验采样，从而统一了插件式方法与生成式逆求解器的观点。在实际应用中，Flower 在多种线性逆问题上实现了最先进的重建质量，且使用几乎相同的超参数。代码已开源：https://github.com/mehrsapo/Flower。
原文摘要 · Abstract (English)
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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