Flow-Driven Optimization Methods for Image Inverse Problems

Flow matching is a recent state-of-the-art framework for generative modeling. A variety of optimization methods that integrate flow matching have been developed for image inverse problems. In this paper, a framework of gradient-related optimization methods is proposed that incorporates the flow matching model for image inverse problems. We introduce a novel regularization term that takes the form of a distance-based function. We prove that the negative gradient of this regularization term corresponds to the velocity field of the flow matching model. Based on this theoretical result, any gradient-related optimization method can be applied to solve optimization problems involving this new regularization term, provided that the data consistency term is differentiable. We propose flow-driven two-step gradient descent (TSGD), a flow-driven fast version of TSGD, flow-driven BCD, and flow-driven ADMM algorithms. Numerically, we evaluate these gradient-related methods on four inverse problems across three datasets. Numerical results demonstrate that FlowDPS, FlowBCD, and FlowADMM achieve superior performance, with FlowBCD and FlowADMM standing out in particular.