无需训练的扩散先验实现快速逆问题求解，速度提升近20倍。
FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems
- 用闭式投影替代迭代优化，一步完成测量空间约束。
- 每噪声层级仅需固定计算量，实测速度提升19.5倍。
- 适合对效率敏感的图像重建任务，无需手写伴随算子。
无训练扩散先验可在不重训练的前提下解决逆问题，但面对非线性前向算子时，数据一致性常依赖重复导数或内层优化/MCMC循环，步长保守导致多轮迭代与大量去噪器/得分函数评估。本文提出一种无训练求解器，以硬测量空间可行性约束（闭式投影）和模型最优解析步长取代内层循环，实现每噪声层级固定计算开销。基于去噪器预测，通过无伴随算子、类似ADMM的分裂策略结合投影与少量最速下降更新，仅需一次VJP及一次JVP或前向差分探测，再经回溯与解耦重退火。证明了步长规则在回溯下的局部模型最优性与下降性，并在局部高斯条件逼近下推导出显式KL界用于模式替换重退火。还开发了潜在空间变体与单参数像素→潜在混合调度。实验表明，性能达竞品水平，峰值信噪比（PSNR）、结构相似性（SSIM）与感知指标（LPIPS）均具竞争力，速度最高提升19.5倍，且无需手工编码伴随算子或内层MCMC。
原文摘要 · Abstract (English)
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.
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