# Solving Inverse Problems in Medical Imaging with Score-Based Generative Models

arXiv: https://arxiv.org/abs/2111.08005 · HTML: https://mlsanity.com/paper/2111.08005/

## Key facts

- Cited by 521 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 52 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## 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)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [SNIPS: Solving Noisy Inverse Problems Stochastically](https://mlsanity.com/paper/2105.14951/) (2021)
- [Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser](https://mlsanity.com/paper/2007.13640/) (2020)
- [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020)
- [TorchRadon: Fast Differentiable Routines for Computed Tomography](https://mlsanity.com/paper/2009.14788/) (2020)
- [Deep Sinogram Completion with Image Prior for Metal Artifact Reduction in CT Images](https://mlsanity.com/paper/2009.07469/) (2020)
- [Robust Compressed Sensing using Generative Models](https://mlsanity.com/paper/2006.09461/) (2020)
- [Deep Generative Adversarial Networks for Compressed Sensing Automates MRI](https://mlsanity.com/paper/1706.00051/) (2017)
- [2-Step Sparse-View CT Reconstruction with a Domain-Specific Perceptual Network](https://mlsanity.com/paper/2012.04743/) (2020)

## Built on by (most cited first, 30 of 521)

- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [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)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions](https://mlsanity.com/paper/2211.01916/) (2022)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Unsupervised Medical Image Translation with Adversarial Diffusion Models](https://mlsanity.com/paper/2207.08208/) (2022)
- [Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistency](https://mlsanity.com/paper/2307.08123/) (2023)
- [Convergence of score-based generative modeling for general data distributions](https://mlsanity.com/paper/2209.12381/) (2022)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Convergence for score-based generative modeling with polynomial complexity](https://mlsanity.com/paper/2206.06227/) (2022)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [The probability flow ODE is provably fast](https://mlsanity.com/paper/2305.11798/) (2023)
- [Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models](https://mlsanity.com/paper/2211.10655/) (2022)
- [Decomposed Diffusion Sampler for Accelerating Large-Scale Inverse Problems](https://mlsanity.com/paper/2303.05754/) (2023)
- [GENIE: Higher-Order Denoising Diffusion Solvers](https://mlsanity.com/paper/2210.05475/) (2022)
- [Score-Based Diffusion Models as Principled Priors for Inverse Imaging](https://mlsanity.com/paper/2304.11751/) (2023)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [Latent Diffusion for Language Generation](https://mlsanity.com/paper/2212.09462/) (2022)
- [Parallel Diffusion Models of Operator and Image for Blind Inverse Problems](https://mlsanity.com/paper/2211.10656/) (2022)

## Abstract (arXiv)

Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes.