Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving

Recent advances in solving have increasingly adopted flow over diffusion models due to their ability to construct straight probability paths from noise to data, thereby enhancing efficiency in both training and inference. However, current flow-based inverse solvers face two primary limitations: (i) they operate directly in pixel space, which demands heavy computational resources for training and restricts scalability to high-resolution images, and (ii) they employ guidance strategies with -agnostic posterior covariances, which can weaken alignment with the generative trajectory and degrade posterior coverage.