# CDiffMR: Can We Replace the Gaussian Noise with K-Space Undersampling for Fast MRI?

arXiv: https://arxiv.org/abs/2306.14350 · HTML: https://mlsanity.com/paper/2306.14350/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 19 of its 23 references that are in the map.
- First posted on arXiv 25 Jun 2023.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Score-based diffusion models for accelerated MRI](https://mlsanity.com/paper/2110.05243/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Unsupervised MRI Reconstruction via Zero-Shot Learned Adversarial Transformers](https://mlsanity.com/paper/2105.08059/) (2021)
- [A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction](https://mlsanity.com/paper/1703.00555/) (2017)
- [Towards performant and reliable undersampled MR reconstruction via diffusion model sampling](https://mlsanity.com/paper/2203.04292/) (2022)
- [Swin Transformer for Fast MRI](https://mlsanity.com/paper/2201.03230/) (2022)
- [AI-based Reconstruction for Fast MRI -- A Systematic Review and Meta-analysis](https://mlsanity.com/paper/2112.12744/) (2021)
- [Over-and-Under Complete Convolutional RNN for MRI Reconstruction](https://mlsanity.com/paper/2106.08886/) (2021)
- [Pyramid Convolutional RNN for MRI Image Reconstruction](https://mlsanity.com/paper/1912.00543/) (2019)
- [ViGU: Vision GNN U-Net for Fast MRI](https://mlsanity.com/paper/2302.10273/) (2023)

## Built on by (most cited first, 12 of 12)

- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [Self-Supervised Adversarial Diffusion Models for Fast MRI Reconstruction](https://mlsanity.com/paper/2406.15656/) (2024)
- [Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics](https://mlsanity.com/paper/2406.13652/) (2024)
- [MRPD: Undersampled MRI reconstruction by prompting a large latent diffusion model](https://mlsanity.com/paper/2402.10609/) (2024)
- [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024)
- [DH-Mamba: Exploring Dual-domain Hierarchical State Space Models for MRI Reconstruction](https://mlsanity.com/paper/2501.08163/) (2025)
- [DuDoUniNeXt: Dual-domain unified hybrid model for single and multi-contrast undersampled MRI reconstruction](https://mlsanity.com/paper/2403.05256/) (2024)
- [Accelerating MRI with Longitudinally-informed Latent Posterior Sampling](https://mlsanity.com/paper/2407.00537/) (2024)
- [CT-SDM: A Sampling Diffusion Model for Sparse-View CT Reconstruction across All Sampling Rates](https://mlsanity.com/paper/2409.01571/) (2024)
- [MS-Glance: Bio-Insipred Non-semantic Context Vectors and their Applications in Supervising Image Reconstruction](https://mlsanity.com/paper/2410.23577/) (2024)
- [High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstruction](https://mlsanity.com/paper/2607.01176/) (2026)
- [Stochastic Finite-Transition Learning and Exploration for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2610.13095/) (2026)

## Abstract (arXiv)

Deep learning has shown the capability to substantially accelerate MRI reconstruction while acquiring fewer measurements. Recently, diffusion models have gained burgeoning interests as a novel group of deep learning-based generative methods. These methods seek to sample data points that belong to a target distribution from a Gaussian distribution, which has been successfully extended to MRI reconstruction. In this work, we proposed a Cold Diffusion-based MRI reconstruction method called CDiffMR. Different from conventional diffusion models, the degradation operation of our CDiffMR is based on textitk-space undersampling instead of adding Gaussian noise, and the restoration network is trained to harness a de-aliaseing function. We also design starting point and data consistency conditioning strategies to guide and accelerate the reverse process. More intriguingly, the pre-trained CDiffMR model can be reused for reconstruction tasks with different undersampling rates. We demonstrated, through extensive numerical and visual experiments, that the proposed CDiffMR can achieve comparable or even superior reconstruction results than state-of-the-art models. Compared to the diffusion model-based counterpart, CDiffMR reaches readily competing results using only 1.6 ~ 3.4% for inference time. The code is publicly available at https://github.com/ayanglab/CDiffMR.