Training-free Medical Image Inverses via Bi-level Guided Diffusion Models

In medical imaging, inverse problems aim to infer highfidelity images from incomplete, noisy measurements, minimizing expenses and risks to patients in clinical settings. Diffusion models have recently emerged as a promising solution to such practical challenges, proving particularly useful for the training-free inference of images from partially acquired measurements in Magnetic Resonance Imaging (MRI) and Computed Tomography (CT). A central challenge, however, is how to guide an unconditional denoised estimate to conform to the measurement information. Existing methods often employ either deficient projection or inefficient posterior approximation, leading to suboptimal performance. In this paper, we propose Bi-level Guided Diffusion Models (BGDM), a zero-shot imaging framework that efficiently steers the image generation process through a bi-level guidance strategy. Specifically, BGDM first approximates an inner-level conditional posterior mean to establish an initial measurement-consistent prediction and then solves an outer-level proximal optimization objective to reinforce the measurement consistency. Our experimental findings, leveraging publicly available MRI and CT datasets, indicate that BGDM is more effective and efficient compared to baseline methods, consistently generating high-fidelity medical images and significantly reducing hallucinatory artifacts in cases of sparse measurements. Code https://github.com/hosseinaskari-cs/BGDM.