# Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstruction

arXiv: https://arxiv.org/abs/2203.03623 · HTML: https://mlsanity.com/paper/2203.03623/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 21 of its 25 references that are in the map.
- First posted on arXiv 5 Mar 2022.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2108.02938/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Learning a Variational Network for Reconstruction of Accelerated MRI Data](https://mlsanity.com/paper/1704.00447/) (2017)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Permutation Invariant Graph Generation via Score-Based Generative Modeling](https://mlsanity.com/paper/2003.00638/) (2020)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [JSR-Net: A Deep Network for Joint Spatial-Radon Domain CT Reconstruction from incomplete data](https://mlsanity.com/paper/1812.00510/) (2018)
- [Trained Model in Supervised Deep Learning is a Conditional Risk Minimizer](https://mlsanity.com/paper/2202.03674/) (2022)

## Built on by (most cited first, 30 of 65)

- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [DiffusionSat: A Generative Foundation Model for Satellite Imagery](https://mlsanity.com/paper/2312.03606/) (2023)
- [GENIE: Higher-Order Denoising Diffusion Solvers](https://mlsanity.com/paper/2210.05475/) (2022)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [MAISI: Medical AI for Synthetic Imaging](https://mlsanity.com/paper/2409.11169/) (2024)
- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [Towards Generalizable Tumor Synthesis](https://mlsanity.com/paper/2402.19470/) (2024)
- [How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control](https://mlsanity.com/paper/2302.03791/) (2023)
- [GSURE-Based Diffusion Model Training with Corrupted Data](https://mlsanity.com/paper/2305.13128/) (2023)
- [Self-Supervised MRI Reconstruction with Unrolled Diffusion Models](https://mlsanity.com/paper/2306.16654/) (2023)
- [Rethinking Diffusion Model for Multi-Contrast MRI Super-Resolution](https://mlsanity.com/paper/2404.04785/) (2024)
- [Hallucination Index: An Image Quality Metric for Generative Reconstruction Models](https://mlsanity.com/paper/2407.12780/) (2024)
- [Diffusion Modeling with Domain-conditioned Prior Guidance for Accelerated MRI and qMRI Reconstruction](https://mlsanity.com/paper/2309.00783/) (2023)
- [SMRD: SURE-based Robust MRI Reconstruction with Diffusion Models](https://mlsanity.com/paper/2310.01799/) (2023)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [Correlated and Multi-frequency Diffusion Modeling for Highly Under-sampled MRI Reconstruction](https://mlsanity.com/paper/2309.00853/) (2023)
- [Timestep-Aware Correction for Quantized Diffusion Models](https://mlsanity.com/paper/2407.03917/) (2024)
- [Text2CT: Towards 3D CT Volume Generation from Free-text Descriptions Using Diffusion Model](https://mlsanity.com/paper/2505.04522/) (2025)
- [Scaling Tumor Segmentation: Best Lessons from Real and Synthetic Data](https://mlsanity.com/paper/2510.14831/) (2025)
- [One-shot Generative Prior in Hankel-k-space for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2208.07181/) (2022)
- [SPIRiT-Diffusion: Self-Consistency Driven Diffusion Model for Accelerated MRI](https://mlsanity.com/paper/2304.05060/) (2023)
- [Convergence Rate Analysis of LION](https://mlsanity.com/paper/2411.07724/) (2024)
- [Uncertainty Estimation and Propagation in Accelerated MRI Reconstruction](https://mlsanity.com/paper/2308.02631/) (2023)
- [A Survey of Emerging Applications of Diffusion Probabilistic Models in MRI](https://mlsanity.com/paper/2311.11383/) (2023)
- [WKGM: Weight-K-space Generative Model for Parallel Imaging Reconstruction](https://mlsanity.com/paper/2205.03883/) (2022)
- [A Conditional Denoising Diffusion Probabilistic Model for Radio Interferometric Image Reconstruction](https://mlsanity.com/paper/2305.09121/) (2023)
- [Segmentation-guided MRI reconstruction for meaningfully diverse reconstructions](https://mlsanity.com/paper/2407.18026/) (2024)
- [Highly Accelerated MRI via Implicit Neural Representation Guided Posterior Sampling of Diffusion Models](https://mlsanity.com/paper/2407.02744/) (2024)
- [Robust Physics-based Deep MRI Reconstruction Via Diffusion Purification](https://mlsanity.com/paper/2309.05794/) (2023)

## Abstract (arXiv)

We propose a novel and unified method, measurement-conditioned denoising diffusion probabilistic model (MC-DDPM), for under-sampled medical image reconstruction based on DDPM. Different from previous works, MC-DDPM is defined in measurement domain (e.g. k-space in MRI reconstruction) and conditioned on under-sampling mask. We apply this method to accelerate MRI reconstruction and the experimental results show excellent performance, outperforming full supervision baseline and the state-of-the-art score-based reconstruction method. Due to its generative nature, MC-DDPM can also quantify the uncertainty of reconstruction. Our code is available on github.