# Physics-Constrained Diffusion Reconstruction with Posterior Correction for Quantitative and Fast PET Imaging

arXiv: https://arxiv.org/abs/2508.14364 · HTML: https://mlsanity.com/paper/2508.14364/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 20 Aug 2025.

## Placed in

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

## Builds on (most cited first, 14 of 14)

- [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)
- [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)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [PET image denoising based on denoising diffusion probabilistic models](https://mlsanity.com/paper/2209.06167/) (2022)
- [DeepPET: A deep encoder-decoder network for directly solving the PET reconstruction inverse problem](https://mlsanity.com/paper/1804.07851/) (2018)
- [Spach Transformer: Spatial and Channel-wise Transformer Based on Local and Global Self-attentions for PET Image Denoising](https://mlsanity.com/paper/2209.03300/) (2022)
- [Direct PET Image Reconstruction Incorporating Deep Image Prior and a Forward Projection Model](https://mlsanity.com/paper/2109.00768/) (2021)
- [Full-dose Whole-body PET Synthesis from Low-dose PET Using High-efficiency Denoising Diffusion Probabilistic Model: PET Consistency Model](https://mlsanity.com/paper/2308.13072/) (2023)
- [2.5D Multi-view Averaging Diffusion Model for 3D Medical Image Translation: Application to Low-count PET Reconstruction with CT-less Attenuation Correction](https://mlsanity.com/paper/2406.08374/) (2024)
- [Unified Noise-aware Network for Low-count PET Denoising](https://mlsanity.com/paper/2304.14900/) (2023)
- [Deep Kernel Representation for Image Reconstruction in PET](https://mlsanity.com/paper/2110.01174/) (2021)
- [Neural KEM: A Kernel Method with Deep Coefficient Prior for PET Image Reconstruction](https://mlsanity.com/paper/2201.01443/) (2022)

## Abstract (arXiv)

Deep learning-based reconstruction of positron emission tomography(PET) data has gained increasing attention in recent years. While these methods achieve fast reconstruction,concerns remain regarding quantitative accuracy and the presence of artifacts,stemming from limited model interpretability,data driven dependence, and overfitting risks.These challenges have hindered clinical adoption.To address them,we propose a conditional diffusion model with posterior physical correction (PET-DPC) for PET image reconstruction. An innovative normalization procedure generates the input Geometric TOF Probabilistic Image (GTP-image),while physical information is incorporated during the diffusion sampling process to perform posterior scatter,attenuation,and random corrections. The model was trained and validated on 300 brain and 50 whole-body PET datasets,a physical phantom,and 20 simulated brain datasets. PET-DPC produced reconstructions closely aligned with fully corrected OSEM images,outperforming end-to-end deep learning models in quantitative metrics and,in some cases, surpassing traditional iterative methods. The model also generalized well to out-of-distribution(OOD) data. Compared to iterative methods,PET-DPC reduced reconstruction time by 50% for brain scans and 85% for whole-body scans. Ablation studies confirmed the critical role of posterior correction in implementing scatter and attenuation corrections,enhancing reconstruction accuracy. Experiments with physical phantoms further demonstrated PET-DPC's ability to preserve background uniformity and accurately reproduce tumor-to-background intensity ratios. Overall,these results highlight PET-DPC as a promising approach for rapid, quantitatively accurate PET reconstruction,with strong potential to improve clinical imaging workflows.