Task-based measures 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, but conventional mathematical SOMs fail to capture realistic anatomy, while data-driven approaches typically require clean data rarely available in clinical tasks. To address this challenge, we propose AMID, an unsupervised Ambient Measurement-Integrated Diffusion 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, an ambient loss is thus designed base 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.