[2603.01591] FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems

Computer Science > Machine Learning arXiv:2603.01591 (cs) [Submitted on 2 Mar 2026] Title:FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems Authors:Minwoo Kim, Seunghyeok Shin, Hongki Lim View a PDF of the paper titled FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems, by Minwoo Kim and 2 other authors View PDF HTML (experimental) Abstract:Training-free diffusion priors enable inverse-problem solvers without retraining, but for nonlinear forward operators data consistency often relies on repeated derivatives or inner optimization/MCMC loops with conservative step sizes, incurring many iterations and denoiser/score evaluations. We propose a training-free solver that replaces these inner loops with a hard measurement-space feasibility constraint (closed-form projection) and an analytic, model-optimal step size, enabling a small, fixed compute budget per noise level. Anchored at the denoiser prediction, the correction is approximated via an adjoint-free, ADMM-style splitting with projection and a few steepest-descent updates, using one VJP and either one JVP or a forward-difference probe, followed by backtracking and decoupled re-annealing. We prove local model optimality and descent under backtracking for the step-size rule, and derive an explicit KL bound for mode-substitution re-annealing under a local Gaussian conditional surrogate. We ...