BARIC: Mean-Response Fitting and Variation Control for Flow-Prior Inverse Problems

Image reconstruction with a pretrained flow prior must reconcile proposed image changes with incomplete or noisy measurements. For a nonlinear measurement operator or latent decoder, fitting one reconstruction does not explicitly control response variation along a proposed change. Our training-free solver, BARIC, evaluates measurements at two symmetrically displaced states along each prior proposal. It moves their center to fit the mean response while penalizing the response difference, with offsets fixed during correction. The penalty discourages opposing probe errors from canceling. We correct two coupled trajectories separately and average their decoded images. We establish fixed-block affine equivalence to pointwise correction in exact arithmetic, analyze local nonlinear departures, and bound the final measurement residual. Across eight inverse problems, BARIC attains the highest reported mean peak signal-to-noise ratio among the compared methods on five pixel-space tasks using CelebA-HQ and seven latent-space tasks using DIV2K, with 100 images per dataset. Objective ablations on 50 images per setting further show higher mean PSNR than pointwise fitting.