FlowLPS: Langevin-Proximal Sampling for Flow-based Inverse Problem Solvers

Deep generative models are powerful priors for imaging inverse problems, but training-free solvers for latent flow models face a practical finite-step trade-off. Optimization-heavy methods quickly improve measurement consistency, but in highly nonlinear latent spaces, their results can depend strongly on where local refinement is initialized, often degrading perceptual realism. In contrast, stochastic sampling methods better preserve posterior exploration, but often require many iterations to obtain sharp, measurement-consistent reconstructions. To address this trade-off, we propose FlowLPS, a training-free latent flow inverse solver based on Langevin-Proximal Sampling. At each reverse step, FlowLPS uses a few Langevin updates to perturb the model-predicted clean estimate in posterior-oriented directions, providing stochastic initializations for local refinement. It then applies local MAP-style proximal refinement to rapidly improve measurement consistency from the Langevin-updated estimate. We additionally use controlled pCN-style re-noising to stabilize the reverse trajectory while retaining trajectory coherence. Experiments on FFHQ and DIV2K across five linear inverse problems show that FlowLPS achieves a strong balance between measurement fidelity and perceptual quality, with additional experiments on pixel-space inverse problems and phase retrieval.