# Likelihood-Scheduled Score-Based Generative Modeling for Fully 3D PET Image Reconstruction

arXiv: https://arxiv.org/abs/2412.04339 · HTML: https://mlsanity.com/paper/2412.04339/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 18 of its 44 references that are in the map.
- First posted on arXiv 5 Dec 2024.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [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)
- [PET image denoising based on denoising diffusion probabilistic models](https://mlsanity.com/paper/2209.06167/) (2022)
- [Improving 3D Imaging with Pre-Trained Perpendicular 2D Diffusion Models](https://mlsanity.com/paper/2303.08440/) (2023)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [Score-Based Generative Models for PET Image Reconstruction](https://mlsanity.com/paper/2308.14190/) (2023)
- [Contrastive Diffusion Model with Auxiliary Guidance for Coarse-to-Fine PET Reconstruction](https://mlsanity.com/paper/2308.10157/) (2023)
- [Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstruction](https://mlsanity.com/paper/2308.14409/) (2023)
- [Patch-Based Diffusion Models Beat Whole-Image Models for Mismatched Distribution Inverse Problems](https://mlsanity.com/paper/2410.11730/) (2024)
- [Joint Diffusion: Mutual Consistency-Driven Diffusion Model for PET-MRI Co-Reconstruction](https://mlsanity.com/paper/2311.14473/) (2023)
- [An autoencoder compression approach for accelerating large-scale inverse problems](https://mlsanity.com/paper/2304.04781/) (2023)

## Built on by (most cited first, 9 of 9)

- [PET Image Reconstruction Using Deep Diffusion Image Prior](https://mlsanity.com/paper/2507.15078/) (2025)
- [Personalized MR-Informed Diffusion Models for 3D PET Image Reconstruction](https://mlsanity.com/paper/2506.03804/) (2025)
- [Supervised Diffusion-Model-Based PET Image Reconstruction](https://mlsanity.com/paper/2506.24034/) (2025)
- [Steerable Conditional Diffusion for Domain Adaptation in PET Image Reconstruction](https://mlsanity.com/paper/2510.13441/) (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)
- [FlowPET: Physics-Informed Symplectic Flow Matching for Low-Count PET Reconstruction](https://mlsanity.com/paper/2607.11104/) (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)

Medical image reconstruction with pre-trained score-based generative models (SGMs) has advantages over other existing state-of-the-art deep-learned reconstruction methods, including improved resilience to different scanner setups and advanced image distribution modeling. SGM-based reconstruction has recently been applied to simulated positron emission tomography (PET) datasets, showing improved contrast recovery for out-of-distribution lesions relative to the state-of-the-art. However, existing methods for SGM-based reconstruction from PET data suffer from slow reconstruction, burdensome hyperparameter tuning and slice inconsistency effects (in 3D). In this work, we propose a practical methodology for fully 3D reconstruction that accelerates reconstruction and reduces the number of critical hyperparameters by matching the likelihood of an SGM's reverse diffusion process to a current iterate of the maximum-likelihood expectation maximization algorithm. Using the example of low-count reconstruction from simulated [18F]DPA-714 datasets, we show our methodology can match or improve on the NRMSE and SSIM of existing state-of-the-art SGM-based PET reconstruction while reducing reconstruction time and the need for hyperparameter tuning. We evaluate our methodology against state-of-the-art supervised and conventional reconstruction algorithms. Finally, we demonstrate a first-ever implementation of SGM-based reconstruction for real 3D PET data, specifically [18F]DPA-714 data, where we integrate perpendicular pre-trained SGMs to eliminate slice inconsistency issues.