Bi-level Guided Diffusion Models for Zero-Shot Medical Imaging Inverse Problems

In the realm of medical imaging, inverse problems aim to infer high-quality images from incomplete, noisy measurements, with the objective of minimizing expenses and risks to patients in clinical settings. The Diffusion Models have recently emerged as a promising approach to such practical challenges, proving particularly useful for the zero-shot inference of images from partially acquired measurements in Magnetic Resonance Imaging (MRI) and Computed Tomography (CT). A central challenge in this approach, however, is how to guide an unconditional prediction to conform to the measurement information. Existing methods rely on deficient projection or inefficient posterior score approximation guidance, which often leads to suboptimal performance. In this paper, we propose \underline{\textbf{B}}i-level \underline{G}uided \underline{D}iffusion \underline{M}odels ({BGDM}), a zero-shot imaging framework that efficiently steers the initial unconditional prediction through a \emph{bi-level} guidance strategy. Specifically, BGDM first approximates an \emph{inner-level} conditional posterior mean as an initial measurement-consistent reference point and then solves an \emph{outer-level} proximal optimization objective to reinforce the measurement consistency. Our experimental findings, using publicly available MRI and CT medical datasets, reveal that BGDM is more effective and efficient compared to the baselines, faithfully generating high-fidelity medical images and substantially reducing hallucinatory artifacts in cases of severe degradation.