  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.
