Establishing Stochastic Object Models from Noisy Data via Ambient Measurement-Integrated Diffusion

Task-based assessments of image quality (IQ) are critical for evaluating medical imaging systems, which must account for randomness, including anatomical variability. Stochastic object models (SOMs) provide a statistical description of such variability. However, conventional mathematical SOMs fail to capture realistic anatomy, while most data-driven approaches typically require clean data, which are rarely available in clinical tasks. To address this challenge, we propose an unsupervised method called Ambient Measurement-Integrated Diffusion (AMID) with noise decoupling, which establishes clean SOMs directly from noisy measurements. AMID introduces a measurement-integrated strategy aligning measurement noise with the diffusion trajectory, and explicitly models coupling between measurement and diffusion noise across steps, and thus an ambient-consistency loss is thus designed based on it to learn clean SOMs. Experiments on real CT and mammography datasets show that AMID outperforms existing methods in generation fidelity and yields more reliable task-based IQ evaluation, demonstrating its potential for unsupervised medical imaging analysis.