Prior as Geometry, Not Generator: Weak-Diffusion Test-Time Reconstruction for Dynamic MRI

Dynamic MRI reconstruction from highly undersampled k-space is a severely ill-posed inverse problem that requires strong measurement consistency, fine spatial recovery, and coherent temporal dynamics. Diffusion priors provide useful population-level regularization, but task-matched spatiotemporal diffusion models are costly to train, while generic pretrained priors may be mismatched to protocols, vendors, or anatomies, leading to hallucination or over-smoothing. Untrained test-time priors such as Time-Dependent Deep Image Prior (TD-DIP) adapt to each scan and naturally couple with data consistency, but can drift toward aliasing artifacts and overfit noise. We propose Geometry-Gated TD-DIP for this weak-diffusion regime, where diffusion is used as a local geometric reference rather than a generative driver. Each TD-DIP update is decomposed into a diffusion-consistent tangent component and a measurement-supported orthogonal innovation component. A self-calibrated gate adaptively regulates the innovation to counter prior mismatch while suppressing noise amplification. We further provide a mismatch-aware analysis showing descent of a local posterior surrogate under explicit conditions. Experiments on cine MRI show consistent gains over diffusion-only, TD-DIP-only, and additive hybrid baselines, especially at high acceleration and under out-of-distribution diffusion priors.