Mean Flows as Controllable Priors for Solving Inverse Problems

Training-free inverse solvers built on flow priors repeatedly need to predict the clean sample reached from an intermediate state along the generative trajectory. Standard flow-matching models expose only an instantaneous velocity, so such predictions need numerical integration or coarse extrapolation. MeanFlow models learn a finite-interval transport map, which lets us use them as controllable priors that move a state across any interval, to the next stage or clean endpoint—all in one evaluation. This interface carries the structure of any flow-based solver onto a MeanFlow prior and makes a new control policy natural: Receding-Horizon State Optimization (RHSO), a model-predictive controller whose decision variable is the generative state itself. A first-order analysis for general data distributions shows how distributing optimization relaxes but retains the prior's implicit regularization. Capacity-matched comparisons in pixel and latent space measure what MeanFlow priors contribute: they surpass flow-matching priors at every stage count tested, most widely with few stages and in latent space. Across five ImageNet restoration tasks, four solvers and four priors, RHSO is best in 35 of 60 task–metric cells and wins 200 of 240 pairwise comparisons. A depth-controlled study attributes most of its gain to distributing optimization over stages, not deeper numerical planning.