FAST-DIPS: 无训练分析步骤和硬约束似然校正用于扩散先验逆问题
FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems
AI总结：
本文提出一种无训练扩散先验求解器，通过硬测量空间可行性约束和分析最优步长，减少迭代次数，实现高效逆问题求解，实验显示在PSNR/SSIM/LPIPS上表现优异，速度提升达19.5倍。
摘要：
免训练扩散先验使逆问题求解者无需重新训练，但非线性前向算子的数据一致性常依赖重复导数或内优化/MCMC循环，导致迭代次数多且去噪器/得分评估消耗大。本文提出一种无训练求解器，用硬测量空间可行性约束（闭式投影）和分析最优步长替代内循环，实现每噪声级别小而固定的计算预算。以去噪器预测为锚点，通过无伴随的ADMM风格分裂与投影及少量最陡下降更新，使用一个VJP和一个JVP或前向差分探针，随后进行回溯和解耦重退火。证明了回溯下步长规则的局部模型最优性和下降性，并在局部高斯条件替代下推导了KL界用于模式替换重退火。还开发了潜在变体和一个参数像素→潜在混合调度。实验在PSNR/SSIM/LPIPS上达到竞争性表现，无手写伴随或内MCMC。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
