Measured-Subspace Consistency: A Plug-and-Play Operator for Diffusion Posterior Sampling in Accelerated MRI Reconstruction

Accelerated magnetic resonance imaging reduces acquisition time, but reconstruction from undersampled k-space can blur diagnostically relevant structures or introduce failures that are not captured by global image metrics. We propose SA-RDM-DC, a Self-Auditing Residual generative Drifting Model with Data Consistency for accelerated knee MRI. The method adapts the newly proposed generative drifting paradigm to accelerated MRI by training a physics-conditioned drift field from the zero-filled reconstruction toward the fully sampled residual correction. It predicts image- and missing-k-space residual corrections, enforces data consistency with acquired k-space, uses frequency-aware and residual drifting supervision to recover fine detail, and produces dense error maps and slice-level risk scores in the same inference pass. We evaluate SA-RDM-DC on multi-coil fastMRI knee data at acceleration factors of 4, 8, and 12, with fastMRI+ pathology annotations for region-level and classifier-based task preservation, and on SKM-TEA for zero-shot and fine-tuned protocol-shift evaluation. Compared with zero-filled reconstruction, UNet-image-SENSE, DC-UNet, Score-Diffusion, ELF-Diff, SENSE-VarNet, and MoDL baselines, SA-RDM-DC achieves the highest SSIM across fastMRI acceleration factors while retaining subsecond per-slice inference and avoiding the long sampling time of iterative diffusion baselines. In pathology-aware analysis, SA-RDM-DC preserves lesion-region structural fidelity and reduces meniscus prediction instability. Its self-auditing scores strongly identify high-error reconstructions on fastMRI and partially transfer as a selective-review signal under SKM-TEA protocol shift. These results support reconstruction evaluation that jointly considers image fidelity, pathology preservation, runtime, and case-specific reliability.

Diffusion posterior sampling conditions diffusion priors on measurements, but data-consistency updates are typically scaled by hand-tuned guidance weights and can destabilize sampling under stiff, operator-dependent curvature. We replace scalar guidance with a per-noise-level damped Gauss--Newton correction computed in diffusion-state coordinates. The correction pulls likelihood gradients back through the denoiser, uses a one-sided curvature model that avoids forward denoiser Jacobians, and applies diffusion-calibrated rank-one damping aligned with the denoiser residual. Each correction is solved with matrix-free GMRES using automatic differentiation, and sampling proceeds with a variance-preserving Langevin transition with a closed-form drift/noise split. On FFHQ and ImageNet across inverse problems, it achieves competitive PSNR/SSIM/LPIPS while running markedly faster than most of the compared baselines; on accelerated MRI reconstruction, it achieves the best PSNR/SSIM among the compared baselines.

Diffusion-based posterior sampling (PS) is a leading framework for imaging inverse problems, combining learned priors with measurement constraints. Yet, its standard formulations rely on instantaneous data-consistent estimates, which induce temporal variability in the reverse dynamics. We reinterpret PS from a dynamical perspective, showing that the standard PS update corresponds to a first-order discretization of the diffusion dynamics plus a residual correction capturing the mismatch between the denoised prediction and the data-consistent estimate. A second-order discretization, however, naturally introduces a temporal correction based on the variation of consecutive estimates. Building on this, we propose LAMP, combining the second-order update with the residual correction characterizing a PS technique. LAMP thus inherits a lagged temporal correction, and it can be implemented as a modular plug-in over the PS backbone. We show that LAMP preserves the structure of a posterior sampler, and we perform a one-step risk analysis to characterize when LAMP improves the reverse transition via a bias-variance trade-off. Experiments across multiple imaging tasks demonstrate consistent improvements over strong baselines such as DiffPIR and DDRM, without increasing the number of denoising evaluations.