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

arXiv: https://arxiv.org/abs/2512.14187 · HTML: https://mlsanity.com/paper/2512.14187/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 20 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Stimulating Diffusion Model for Image Denoising via Adaptive Embedding and Ensembling](https://mlsanity.com/paper/2307.03992/) (2023)
- [Learning stochastic object models from medical imaging measurements by use of advanced ambient generative adversarial networks](https://mlsanity.com/paper/2106.14324/) (2021)
- [MedDiff-FM: A Diffusion-based Foundation Model for Versatile Medical Image Applications](https://mlsanity.com/paper/2410.15432/) (2024)
- [AmbientCycleGAN for Establishing Interpretable Stochastic Object Models Based on Mathematical Phantoms and Medical Imaging Measurements](https://mlsanity.com/paper/2402.01171/) (2024)
- [Ambient Denoising Diffusion Generative Adversarial Networks for Establishing Stochastic Object Models from Noisy Image Data](https://mlsanity.com/paper/2501.19094/) (2025)
- [Dual Path Learning -- learning from noise and context for medical image denoising](https://mlsanity.com/paper/2507.19035/) (2025)

## Abstract (arXiv)

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.