FLOWER: A Flow-Matching Solver for Inverse Problems
This work addresses the challenge of efficient and consistent reconstruction in inverse problems for fields like imaging and signal processing, representing a novel integration of methods rather than an incremental improvement.
The paper tackles the problem of solving inverse problems by introducing FLOWER, a flow-matching solver that leverages pre-trained flow models to produce reconstructions consistent with observed measurements, achieving state-of-the-art reconstruction quality with nearly identical hyperparameters across various tasks.
We introduce Flower, a solver for 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 inverse problems.