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

2026-03-02

AI Summary

This work addresses the computational inefficiency of existing methods for solving inverse problems with diffusion priors under nonlinear forward operators, which often rely on expensive repeated derivative evaluations or inner-loop optimization/MCMC sampling. The authors propose a training-free solver that replaces inner loops with hard constraint projections in measurement space and analytically derived optimal step sizes, yielding fixed and low per-noise-level computational cost. The key innovation lies in the first joint optimization framework that is adjoint-free, combining analytical step sizes with hard constraints. This approach integrates ADMM splitting, reannealing, and a hybrid latent/pixel-space scheduling strategy to guarantee local optimality and descent properties, while also enabling a derived KL error bound. Experiments demonstrate state-of-the-art PSNR, SSIM, and LPIPS performance in image reconstruction, achieving up to 19.5× acceleration without requiring hand-coded adjoints or MCMC sampling.

Technology Category

• Search and Optimization: Non-convex Optimization
• Computer Vision: Learning & Optimization for CV
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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 also develop a latent variant and a one-parameter pixel$\rightarrow$latent hybrid schedule. Experiments achieve competitive PSNR/SSIM/LPIPS with up to 19.5$\times$ speedup, without hand-coded adjoints or inner MCMC.

Problem

• diffusion-prior inverse problems
• nonlinear forward operators
• data consistency
• inner optimization loops
• computational efficiency

Innovation

• adjoint-free
• hard-constrained projection
• analytic step size
• diffusion prior
• training-free inverse solver