# Score-Based Generative Models for PET Image Reconstruction

arXiv: https://arxiv.org/abs/2308.14190 · HTML: https://mlsanity.com/paper/2308.14190/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 30 of its 77 references that are in the map.
- First posted on arXiv 27 Aug 2023.

## Placed in

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

## Builds on (most cited first, 30 of 30)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [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)
- [Brain Imaging Generation with Latent Diffusion Models](https://mlsanity.com/paper/2209.07162/) (2022)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Solving 3D Inverse Problems using Pre-trained 2D Diffusion Models](https://mlsanity.com/paper/2211.10655/) (2022)
- [Reflected Diffusion Models](https://mlsanity.com/paper/2304.04740/) (2023)
- [PET image denoising based on denoising diffusion probabilistic models](https://mlsanity.com/paper/2209.06167/) (2022)
- [Test-Time Training Can Close the Natural Distribution Shift Performance Gap in Deep Learning Based Compressed Sensing](https://mlsanity.com/paper/2204.07204/) (2022)
- [MRI Reconstruction with Side Information using Diffusion Models](https://mlsanity.com/paper/2303.14795/) (2023)
- [Denoising Score-Matching for Uncertainty Quantification in Inverse Problems](https://mlsanity.com/paper/2011.08698/) (2020)
- [List-Mode PET Image Reconstruction Using Deep Image Prior](https://mlsanity.com/paper/2204.13404/) (2022)
- [Learning Gradually Non-convex Image Priors Using Score Matching](https://mlsanity.com/paper/2302.10502/) (2023)

## Built on by (most cited first, 22 of 22)

- [Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstruction](https://mlsanity.com/paper/2308.14409/) (2023)
- [Likelihood-Scheduled Score-Based Generative Modeling for Fully 3D PET Image Reconstruction](https://mlsanity.com/paper/2412.04339/) (2024)
- [PET Image Reconstruction Using Deep Diffusion Image Prior](https://mlsanity.com/paper/2507.15078/) (2025)
- [Physics-Inspired Generative Models in Medical Imaging: A Review](https://mlsanity.com/paper/2407.10856/) (2024)
- [Efficient Bayesian Computation Using Plug-and-Play Priors for Poisson Inverse Problems](https://mlsanity.com/paper/2503.16222/) (2025)
- [Personalized MR-Informed Diffusion Models for 3D PET Image Reconstruction](https://mlsanity.com/paper/2506.03804/) (2025)
- [A Stability Benchmark of Generative Regularizers for Inverse Problems](https://mlsanity.com/paper/2605.10076/) (2026)
- [Mixed Noise and Posterior Estimation with Conditional DeepGEM](https://mlsanity.com/paper/2402.02964/) (2024)
- [Pseudo-MRI-Guided PET Image Reconstruction Method Based on a Diffusion Probabilistic Model](https://mlsanity.com/paper/2403.18139/) (2024)
- [Generative-Model-Based Fully 3D PET Image Reconstruction by Conditional Diffusion Sampling](https://mlsanity.com/paper/2412.04319/) (2024)
- [Multi-Subject Image Synthesis as a Generative Prior for Single-Subject PET Image Reconstruction](https://mlsanity.com/paper/2412.04324/) (2024)
- [Supervised Diffusion-Model-Based PET Image Reconstruction](https://mlsanity.com/paper/2506.24034/) (2025)
- [TauGenNet: Plasma-Driven Tau PET Image Synthesis via Text-Guided 3D Diffusion Models](https://mlsanity.com/paper/2509.04269/) (2025)
- [Steerable Conditional Diffusion for Domain Adaptation in PET Image Reconstruction](https://mlsanity.com/paper/2510.13441/) (2025)
- [PET-Adapter: Test-Time Domain Adaptation for Full and Limited-Angle PET Image Reconstruction](https://mlsanity.com/paper/2605.08030/) (2026)
- [Two-stage deep learning framework for the restoration of incomplete-ring PET images](https://mlsanity.com/paper/2504.00816/) (2025)
- [Score-based Generative Diffusion Models to Synthesize Full-dose FDG Brain PET from MRI in Epilepsy Patients](https://mlsanity.com/paper/2506.11297/) (2025)
- [Bregman geometry-aware split Gibbs sampling for Bayesian Poisson inverse problems](https://mlsanity.com/paper/2511.12257/) (2025)
- [CT-Conditioned Diffusion Prior with Physics-Constrained Sampling for PET Super-Resolution](https://mlsanity.com/paper/2603.13901/) (2026)
- [HDDPM: Heteroscedastic Denoising Diffusion Probabilistic Model for Quantitative Low-Count Brain PET Recovery](https://mlsanity.com/paper/2606.28513/) (2026)
- [Flow Matching-Based PET Image Reconstruction](https://mlsanity.com/paper/2608.20112/) (2026)
- [Manifold-Constrained PET Reconstruction with Learned Flow-Matching Priors](https://mlsanity.com/paper/2608.29158/) (2026)

## Abstract (arXiv)

Score-based generative models have demonstrated highly promising results for medical image reconstruction tasks in magnetic resonance imaging or computed tomography. However, their application to Positron Emission Tomography (PET) is still largely unexplored. PET image reconstruction involves a variety of challenges, including Poisson noise with high variance and a wide dynamic range. To address these challenges, we propose several PET-specific adaptations of score-based generative models. The proposed framework is developed for both 2D and 3D PET. In addition, we provide an extension to guided reconstruction using magnetic resonance images. We validate the approach through extensive 2D and 3D textitin-silico experiments with a model trained on patient-realistic data without lesions, and evaluate on data without lesions as well as out-of-distribution data with lesions. This demonstrates the proposed method's robustness and significant potential for improved PET reconstruction.