# Self-Score: Self-Supervised Learning on Score-Based Models for MRI Reconstruction

arXiv: https://arxiv.org/abs/2209.00835 · HTML: https://mlsanity.com/paper/2209.00835/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 16 of its 37 references that are in the map.
- First posted on arXiv 2 Sep 2022.

## Placed in

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

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [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)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [Noisier2Noise: Learning to Denoise from Unpaired Noisy Data](https://mlsanity.com/paper/1910.11908/) (2019)
- [Deep Low-rank plus Sparse Network for Dynamic MR Imaging](https://mlsanity.com/paper/2010.13677/) (2020)
- [LORAKI: Autocalibrated Recurrent Neural Networks for Autoregressive MRI Reconstruction in k-Space](https://mlsanity.com/paper/1904.09390/) (2019)
- [Self-Supervised Physics-Based Deep Learning MRI Reconstruction Without Fully-Sampled Data](https://mlsanity.com/paper/1910.09116/) (2019)
- [Unsupervised Deep Learning Methods for Biological Image Reconstruction and Enhancement](https://mlsanity.com/paper/2105.08040/) (2021)
- [Equilibrated Zeroth-Order Unrolled Deep Networks for Accelerated MRI](https://mlsanity.com/paper/2112.09891/) (2021)

## Built on by (most cited first, 23 of 23)

- [Diffusion Models for Medical Image Analysis: A Comprehensive Survey](https://mlsanity.com/paper/2211.07804/) (2022)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Efficient Diffusion Models: A Comprehensive Survey from Principles to Practices](https://mlsanity.com/paper/2410.11795/) (2024)
- [Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Data](https://mlsanity.com/paper/2305.01166/) (2023)
- [Self-Supervised MRI Reconstruction with Unrolled Diffusion Models](https://mlsanity.com/paper/2306.16654/) (2023)
- [Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data](https://mlsanity.com/paper/2403.08728/) (2024)
- [DiffBoost: Enhancing Medical Image Segmentation via Text-Guided Diffusion Model](https://mlsanity.com/paper/2310.12868/) (2023)
- [Score Priors Guided Deep Variational Inference for Unsupervised Real-World Single Image Denoising](https://mlsanity.com/paper/2308.04682/) (2023)
- [Learning Fourier-Constrained Diffusion Bridges for MRI Reconstruction](https://mlsanity.com/paper/2308.01096/) (2023)
- [A Survey of Emerging Applications of Diffusion Probabilistic Models in MRI](https://mlsanity.com/paper/2311.11383/) (2023)
- [Deep unfolding as iterative regularization for imaging inverse problems](https://mlsanity.com/paper/2211.13452/) (2022)
- [Highly Accelerated MRI via Implicit Neural Representation Guided Posterior Sampling of Diffusion Models](https://mlsanity.com/paper/2407.02744/) (2024)
- [Score-based Diffusion Models With Self-supervised Learning For Accelerated 3D Multi-contrast Cardiac Magnetic Resonance Imaging](https://mlsanity.com/paper/2310.04669/) (2023)
- [Joint Supervised and Self-supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2311.15856/) (2023)
- [Robust multi-coil MRI reconstruction via self-supervised denoising](https://mlsanity.com/paper/2411.12919/) (2024)
- [Subspace Implicit Neural Representations for Real-Time Cardiac Cine MR Imaging](https://mlsanity.com/paper/2412.12742/) (2024)
- [Arbitrary Reduction of MRI Inter-slice Spacing Using Hierarchical Feature Conditional Diffusion](https://mlsanity.com/paper/2304.07756/) (2023)
- [Poisson-Gaussian Holographic Phase Retrieval with Score-based Image Prior](https://mlsanity.com/paper/2305.07712/) (2023)
- [JSMoCo: Joint Coil Sensitivity and Motion Correction in Parallel MRI with a Self-Calibrating Score-Based Diffusion Model](https://mlsanity.com/paper/2310.09625/) (2023)
- [Re-Visible Dual-Domain Self-Supervised Deep Unfolding Network for MRI Reconstruction](https://mlsanity.com/paper/2501.03737/) (2025)
- [Bayesian imaging inverse problem with SA-Roundtrip prior via HMC-pCN sampler](https://mlsanity.com/paper/2310.17817/) (2023)
- [Dual-domain Multi-path Self-supervised Diffusion Model for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2503.18836/) (2025)

## Abstract (arXiv)

Recently, score-based diffusion models have shown satisfactory performance in MRI reconstruction. Most of these methods require a large amount of fully sampled MRI data as a training set, which, sometimes, is difficult to acquire in practice. This paper proposes a fully-sampled-data-free score-based diffusion model for MRI reconstruction, which learns the fully sampled MR image prior in a self-supervised manner on undersampled data. Specifically, we first infer the fully sampled MR image distribution from the undersampled data by Bayesian deep learning, then perturb the data distribution and approximate their probability density gradient by training a score function. Leveraging the learned score function as a prior, we can reconstruct the MR image by performing conditioned Langevin Markov chain Monte Carlo (MCMC) sampling. Experiments on the public dataset show that the proposed method outperforms existing self-supervised MRI reconstruction methods and achieves comparable performances with the conventional (fully sampled data trained) score-based diffusion methods.