# Learning to Reconstruct Accelerated MRI Through K-space Cold Diffusion without Noise

arXiv: https://arxiv.org/abs/2311.10162 · HTML: https://mlsanity.com/paper/2311.10162/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 28 of its 33 references that are in the map.
- First posted on arXiv 16 Nov 2023.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (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)
- [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)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [Efficient Diffusion Training via Min-SNR Weighting Strategy](https://mlsanity.com/paper/2303.09556/) (2023)
- [End-to-End Variational Networks for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2004.06688/) (2020)
- [Conversion Between CT and MRI Images Using Diffusion and Score-Matching Models](https://mlsanity.com/paper/2209.12104/) (2022)
- [Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstruction](https://mlsanity.com/paper/2203.03623/) (2022)
- [GrappaNet: Combining Parallel Imaging with Deep Learning for Multi-Coil MRI Reconstruction](https://mlsanity.com/paper/1910.12325/) (2019)
- [Few-Shot Diffusion Models](https://mlsanity.com/paper/2205.15463/) (2022)
- [Dual-domain Cascade of U-nets for Multi-channel Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1911.01458/) (2019)
- [A Hybrid Frequency-domain/Image-domain Deep Network for Magnetic Resonance Image Reconstruction](https://mlsanity.com/paper/1810.12473/) (2018)
- [Machine Learning in Magnetic Resonance Imaging: Image Reconstruction](https://mlsanity.com/paper/2012.05303/) (2020)

## Built on by (most cited first, 4 of 4)

- [Accelerating MRI with Longitudinally-informed Latent Posterior Sampling](https://mlsanity.com/paper/2407.00537/) (2024)
- [Few-Shot Deployment of Pretrained MRI Transformers in Brain Imaging Tasks](https://mlsanity.com/paper/2508.05783/) (2025)
- [High-dimensional Embedding Prior for Noisy K-space Domain MRIReconstruction](https://mlsanity.com/paper/2607.01176/) (2026)
- [Dense Temporal Contrast Synthesis via Conditioned Latent Transport](https://mlsanity.com/paper/2607.29394/) (2026)

## Abstract (arXiv)

Deep learning-based MRI reconstruction models have achieved superior performance these days. Most recently, diffusion models have shown remarkable performance in image generation, in-painting, super-resolution, image editing and more. As a generalized diffusion model, cold diffusion further broadens the scope and considers models built around arbitrary image transformations such as blurring, down-sampling, etc. In this paper, we propose a k-space cold diffusion model that performs image degradation and restoration in k-space without the need for Gaussian noise. We provide comparisons with multiple deep learning-based MRI reconstruction models and perform tests on a well-known large open-source MRI dataset. Our results show that this novel way of performing degradation can generate high-quality reconstruction images for accelerated MRI.