Tethered Predictive-Inertial Proposals with Objective Verification for Diffusion-Prior Inverse Problems

Training-free diffusion priors are powerful for inverse problems, but measurement guidance during reverse sampling is local: aggressive updates can improve immediate data fit while disrupting later denoising. We introduce a tethered predictive-inertial correction rule that separates proposal generation from acceptance. At each corrected step, the denoiser prediction anchors a frozen clean-space objective combining measurement fit with a noise-level-dependent tether. Heavy-ball dynamics with diffusion-scale predictive smoothing generate clean-state candidates; a separate verifier evaluates a finite dyadic set using the original unsmoothed objective, with the denoiser prediction retained as fallback. The accepted clean state is re-noised to continue sampling. The rule applies to pixel and latent diffusion with differentiable measurement operators, requires no retraining, and adds no denoiser calls inside the correction loop. We analyze when smoothing is inactive, how it changes nonlinear or decoder-composed proposal landscapes, and how objective verification yields local nonincrease, scale robustness, and displacement control. Across natural-image and accelerated MRI benchmarks, the method achieves competitive reconstruction quality with favorable speed--quality trade--offs, often reducing runtime relative to optimization-heavy diffusion solvers. On fastMRI knee reconstruction, it attains the strongest PSNR among compared methods at both acceleration factors.