mlsanityData to 7 Oct 2026

Score-based diffusion models for accelerated MRI

arXiv 2110.05243 ↗First posted 8 Oct 2021eess.IV cs.AI cs.CVcited by 308

On the map: Diffusion models → Medical imaging and segmentation

Abstract (arXiv)

Score-based diffusion models provide a powerful way to model images using the gradient of the data distribution. Leveraging the learned score function as a prior, here we introduce a way to sample data from a conditional distribution given the measurements, such that the model can be readily used for solving inverse problems in imaging, especially for accelerated MRI. In short, we train a continuous time-dependent score function with denoising score matching. Then, at the inference stage, we iterate between numerical SDE solver and data consistency projection step to achieve reconstruction. Our model requires magnitude images only for training, and yet is able to reconstruct complex-valued data, and even extends to parallel imaging. The proposed method is agnostic to sub-sampling patterns, and can be used with any sampling schemes. Also, due to its generative nature, our approach can quantify uncertainty, which is not possible with standard regression settings. On top of all the advantages, our method also has very strong performance, even beating the models trained with full supervision. With extensive experiments, we verify the superiority of our method in terms of quality and practicality.

Key facts. Cited by 308 papers in the map (data through 7 Oct 2026). Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models. Builds on 40 of its 75 references that are in the map. First posted on arXiv 8 Oct 2021.

Builds on

40 of 75 references.

References · 40

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2020Denoising Diffusion Implicit Modelscited by 9,655
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  6. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  7. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  8. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  9. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  10. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  11. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,736
  12. 2018Neural Ordinary Differential Equationscited by 3,733
28 more
  1. 2019Analyzing and Improving the Image Quality of StyleGANcited by 3,580
  2. 2017Progressive Growing of GANs for Improved Quality, Stability, and Variationcited by 2,967
  3. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  4. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
  5. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  6. 2016Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Networkcited by 1,898
  7. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  8. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  9. 2021Variational Diffusion Modelscited by 1,145
  10. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,036
  11. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  12. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Modelscited by 634
  13. 2018fastMRI: An Open Dataset and Benchmarks for Accelerated MRIcited by 464
  14. 2019Making Convolutional Networks Shift-Invariant Againcited by 390
  15. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  16. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  17. 2021How to Train Your Energy-Based Modelscited by 271
  18. 2020Permutation Invariant Graph Generation via Score-Based Generative Modelingcited by 263
  19. 2020End-to-End Variational Networks for Accelerated MRI Reconstructioncited by 201
  20. 2019Invertible generative models for inverse problems: mitigating representation error and dataset biascited by 93
  21. 2020DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Priorcited by 72
  22. 2020Bayesian Image Reconstruction using Deep Generative Modelscited by 29
  23. 2021fastMRI+: Clinical Pathology Annotations for Knee and Brain Fully Sampled Multi-Coil MRI Datacited by 29
  24. 2020Unpaired Deep Learning for Accelerated MRI using Optimal Transport Driven CycleGANcited by 28
  25. 2020AR-DAE: Towards Unbiased Neural Entropy Gradient Estimationcited by 19
  26. 2020Denoising Score-Matching for Uncertainty Quantification in Inverse Problemscited by 11
  27. 2021MRI Reconstruction Using Deep Energy-Based Modelcited by 8
  28. 2020Fast Variable Density Poisson-Disc Sample Generation with Directional Variationcited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 32; 2023: 73; 2024: 97; 2025: 67; 2026: 38.

308 papers.

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By area:

  1. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  2. 2022Diffusion Models: A Comprehensive Survey of Methods and Applicationscited by 1,107
  3. 2022Diffusion Models in Vision: A Surveycited by 1,008
  4. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contractioncited by 306
  5. 2022Diffusion Models for Medical Image Analysis: A Comprehensive Surveycited by 269
  6. 2022A Survey on Generative Diffusion Modelcited by 238
  7. 2022Unsupervised Medical Image Translation with Adversarial Diffusion Modelscited by 191
  8. 2024A Survey on Diffusion Models for Inverse Problemscited by 173
  9. 2023PTQD: Accurate Post-Training Quantization for Diffusion Modelscited by 167
  10. 2022Generative Modelling With Inverse Heat Dissipationcited by 164
  11. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  12. 2022Solving 3D Inverse Problems using Pre-trained 2D Diffusion Modelscited by 130
38 more
  1. 2023Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problemscited by 129
  2. 2022GENIE: Higher-Order Denoising Diffusion Solverscited by 127
  3. 2023Score-Based Diffusion Models as Principled Priors for Inverse Imagingcited by 126
  4. 2022Adaptive Diffusion Priors for Accelerated MRI Reconstructioncited by 117
  5. 2022Parallel Diffusion Models of Operator and Image for Blind Inverse Problemscited by 113
  6. 2024TFG: Unified Training-Free Guidance for Diffusion Modelscited by 103
  7. 2022Exploring Chemical Space with Score-based Out-of-distribution Generationcited by 95
  8. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  9. 2024Constrained Synthesis with Projected Diffusion Modelscited by 83
  10. 2022DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstructioncited by 73
  11. 2024Diffusion Models in Low-Level Vision: A Surveycited by 73
  12. 2024An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimizationcited by 72
  13. 2023Prompt-tuning latent diffusion models for inverse problemscited by 70
  14. 2023Generative AI for Medical Imaging: extending the MONAI Frameworkcited by 68
  15. 2024Jailbreaking Prompt Attack: A Controllable Adversarial Attack against Diffusion Modelscited by 68
  16. 2025InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciencescited by 67
  17. 2022MR Image Denoising and Super-Resolution Using Regularized Reverse Diffusioncited by 66
  18. 2022Measurement-conditioned Denoising Diffusion Probabilistic Model for Under-sampled Medical Image Reconstructioncited by 64
  19. 2022Towards performant and reliable undersampled MR reconstruction via diffusion model samplingcited by 59
  20. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problemscited by 58
  21. 2022PET image denoising based on denoising diffusion probabilistic modelscited by 57
  22. 2023CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problemscited by 54
  23. 2023Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Modelscited by 53
  24. 2022ReconFormer: Accelerated MRI Reconstruction Using Recurrent Transformercited by 52
  25. 2022Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Modelscited by 50
  26. 2023Score-based Causal Representation Learning with Interventionscited by 49
  27. 2024Tutorial on Diffusion Models for Imaging and Visioncited by 49
  28. 2023Face Animation with an Attribute-Guided Diffusion Modelcited by 48
  29. 2025Inference-time Scaling of Diffusion Models through Classical Searchcited by 48
  30. 2022Bayesian MRI Reconstruction with Joint Uncertainty Estimation using Diffusion Modelscited by 46
  31. 2022High-Frequency Space Diffusion Models for Accelerated MRIcited by 41
  32. 2023Solving Inverse Problems with Score-Based Generative Priors learned from Noisy Datacited by 40
  33. 2023GSURE-Based Diffusion Model Training with Corrupted Datacited by 40
  34. 2024Curriculum Direct Preference Optimization for Diffusion and Consistency Modelscited by 36
  35. 2025MagicMirror: ID-Preserved Video Generation in Video Diffusion Transformerscited by 32
  36. 2023User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systemscited by 30
  37. 2023Controllable Music Production with Diffusion Models and Guidance Gradientscited by 29
  38. 2024Rethinking Diffusion Model for Multi-Contrast MRI Super-Resolutioncited by 29

50 most cited of 308 All 308 (JSON)

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  1. 2024Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction
  2. 2025Measurement Score-Based Diffusion Model
  3. 2024Efficient Denoising using Score Embedding in Score-based Diffusion Models
  4. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensions
  5. 2025Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problems
  6. 2025Diff-Unfolding: A Model-Based Score Learning Framework for Inverse Problems
  7. 2025Faster Diffusion Models via Higher-Order Approximation
  8. 2023Reflected Diffusion Models