Stochastic Generative Plug-and-Play Priors

Plug-and-Play diffusion prior (PnPDP) frameworks have emerged as a powerful paradigm for solving imaging inverse problems by treating pretrained generative models as modular priors. However, we identify a critical flaw in prevailing PnP solvers (e.g., based on HQS or Proximal Gradient): they function as memoryless operators, updating estimates solely based on instantaneous gradients. This lack of historical tracking inevitably leads to non-vanishing steady-state bias, where the reconstruction fails to strictly satisfy physical measurements under heavy corruption. To resolve this, we propose Dual-Coupled PnP Diffusion (DC-PnPDP), which restores the classical dual variable to provide integral feedback, progressively enforce agreement between the data-consistency and prior. However, this rigorous geometric coupling introduces a secondary challenge: the accumulated dual residuals exhibit spectrally colored, structured artifacts that violate the Additive White Gaussian Noise (AWGN) assumption of diffusion priors, causing severe hallucinations. To bridge this gap, we introduce Spectral Homogenization (SH), a frequency-domain adaptation mechanism that modulates these structured residuals into statistically compliant pseudo-AWGN inputs. This effectively aligns the solver's rigorous optimization trajectory with the denoiser's valid statistical manifold. Extensive experiments on CT and MRI reconstruction demonstrate that our approach resolves the bias-hallucination trade-off, achieving state-of-the-art fidelity with significantly accelerated convergence. The code is available at https://github.com/duchenhe/DC-PnPDP

Modern image restoration methods increasingly rely on large-scale supervised training, yet clean targets are often prohibitively difficult to obtain in scientific imaging modalities such as hyperspectral imaging (HSI) and magnetic resonance imaging (MRI). Plug-and-play ADMM (PnP-ADMM) with pretrained diffusion priors offers a promising alternative, but the learned prior distribution can mismatch both the target scientific image distribution and the distribution of ADMM denoiser inputs induced by dual feedback. To mitigate these mismatches, we propose $\mathrm{S}^3$-PnP, a self-supervised plug-and-play restoration framework that learns a score prior directly from observation-derived ADMM intermediate states, without clean training targets or externally pretrained weights. Specifically, the learned score corrects the input to the analytical prior update, combining observation-driven corrections with analytical regularization. We further analyze the convergence and reconstruction error of the corrected ADMM algorithm assuming an ideal score and quadratic data fidelity. Experiments on reference-guided HSI restoration, single-image HSI denoising, and MRI denoising demonstrate consistent improvements over competing methods.

Pretrained diffusion models represent image distributions through a continuum of progressively smoothed distributions. This multiscale structure organizes generation from global structure to fine detail and supports high-quality, diverse samples. We exploit the same multiscale diffusion prior for linear imaging inverse problems. Rather than using the pretrained model only as a denoiser in an outer iteration, we define a surrogate likelihood whose center is aligned with the clean-image coordinate and whose covariance accounts for residual diffusion uncertainty. This construction defines an explicit surrogate posterior path, from which we derive continuous posterior dynamics. A tunable Langevin component supports target tracking and allows the amount of posterior exploration to be adapted to the application. We prove endpoint consistency and a finite-horizon tracking bound and, in the exact-score setting, first-order weak accuracy. For computation, we derive the Posterior-Dynamics Implicit--Explicit sampler (PD-IMEX), a stable method using one score evaluation per diffusion scale and an implicit data-consistency update. Experiments on deblurring, super-resolution, and inpainting show strong reconstruction quality at 100 score evaluations, coarse-grid stability, and controllable fidelity--diversity behavior.