# GR-Diffusion: 3D Gaussian Representation Meets Diffusion in Whole-Body PET Reconstruction

arXiv: https://arxiv.org/abs/2602.11653 · HTML: https://mlsanity.com/paper/2602.11653/

## Key facts

- Cited by 1 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 45 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## 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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction](https://mlsanity.com/paper/2405.20693/) (2024)
- [Radiative Gaussian Splatting for Efficient X-ray Novel View Synthesis](https://mlsanity.com/paper/2403.04116/) (2024)
- [Baking Gaussian Splatting into Diffusion Denoiser for Fast and Scalable Single-stage Image-to-3D Generation and Reconstruction](https://mlsanity.com/paper/2411.14384/) (2024)
- [Learning 3D Gaussians for Extremely Sparse-View Cone-Beam CT Reconstruction](https://mlsanity.com/paper/2407.01090/) (2024)
- [Three-Dimensional MRI Reconstruction with Gaussian Representations: Tackling the Undersampling Problem](https://mlsanity.com/paper/2502.06510/) (2025)
- [Discretized Gaussian Representation for Tomographic Reconstruction](https://mlsanity.com/paper/2411.04844/) (2024)
- [X2-Gaussian: 4D Radiative Gaussian Splatting for Continuous-time Tomographic Reconstruction](https://mlsanity.com/paper/2503.21779/) (2025)
- [From Coarse to Fine: Learnable Discrete Wavelet Transforms for Efficient 3D Gaussian Splatting](https://mlsanity.com/paper/2506.23042/) (2025)
- [PET Image Reconstruction Using Deep Diffusion Image Prior](https://mlsanity.com/paper/2507.15078/) (2025)
- [Diffusion Transformer Model With Compact Prior for Low-dose PET Reconstruction](https://mlsanity.com/paper/2407.00944/) (2024)
- [GR-Gaussian: Graph-Based Radiative Gaussian Splatting for Sparse-View CT Reconstruction](https://mlsanity.com/paper/2508.02408/) (2025)
- [GEM: 3D Gaussian Splatting for Efficient and Accurate Cryo-EM Reconstruction](https://mlsanity.com/paper/2509.25075/) (2025)
- [Time-resolved dynamic CBCT reconstruction using prior-model-free spatiotemporal Gaussian representation (PMF-STGR)](https://mlsanity.com/paper/2503.22139/) (2025)
- [3D Gaussian Adaptive Reconstruction for Fourier Light-Field Microscopy](https://mlsanity.com/paper/2505.12875/) (2025)
- [WIPES: Wavelet-based Visual Primitives](https://mlsanity.com/paper/2508.12615/) (2025)
- [DIGS: Dynamic CBCT Reconstruction using Deformation-Informed 4D Gaussian Splatting and a Low-Rank Free-Form Deformation Model](https://mlsanity.com/paper/2506.22280/) (2025)
- [DenoiseGS: Gaussian Reconstruction Model for Burst Denoising](https://mlsanity.com/paper/2511.22939/) (2025)

## Built on by (most cited first, 1 of 1)

- [PAGS: Autofocusing Photoacoustic Tomography via Speed-of-Sound-Adaptive Gaussian Splatting](https://mlsanity.com/paper/2608.25472/) (2026)

## Abstract (arXiv)

Positron emission tomography (PET) reconstruction is a critical challenge in molecular imaging, often hampered by noise amplification, structural blurring, and detail loss due to sparse sampling and the ill-posed nature of inverse problems. The three-dimensional discrete Gaussian representation (GR), which efficiently encodes 3D scenes using parameterized discrete Gaussian distributions, has shown promise in computer vision. In this work, we pro-pose a novel GR-Diffusion framework that synergistically integrates the geometric priors of GR with the generative power of diffusion models for 3D low-dose whole-body PET reconstruction. GR-Diffusion employs GR to generate a reference 3D PET image from projection data, establishing a physically grounded and structurally explicit benchmark that overcomes the low-pass limitations of conventional point-based or voxel-based methods. This reference image serves as a dual guide during the diffusion process, ensuring both global consistency and local accuracy. Specifically, we employ a hierarchical guidance mechanism based on the GR reference. Fine-grained guidance leverages differences to refine local details, while coarse-grained guidance uses multi-scale difference maps to correct deviations. This strategy allows the diffusion model to sequentially integrate the strong geometric prior from GR and recover sub-voxel information. Experimental results on the UDPET and Clinical datasets with varying dose levels show that GR-Diffusion outperforms state-of-the-art methods in enhancing 3D whole-body PET image quality and preserving physiological details.