# HDDPM: Heteroscedastic Denoising Diffusion Probabilistic Model for Quantitative Low-Count Brain PET Recovery

arXiv: https://arxiv.org/abs/2606.28513 · HTML: https://mlsanity.com/paper/2606.28513/

## 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 8 of its 18 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Placed in

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

## Builds on (most cited first, 8 of 8)

- [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)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Score-Based Generative Models for PET Image Reconstruction](https://mlsanity.com/paper/2308.14190/) (2023)
- [Unified Noise-aware Network for Low-count PET Denoising](https://mlsanity.com/paper/2304.14900/) (2023)
- [Dose-aware Diffusion Model for 3D PET Image Denoising: Multi-institutional Validation with Reader Study and Real Low-dose Data](https://mlsanity.com/paper/2405.12996/) (2024)
- [A Noise-level-aware Framework for PET Image Denoising](https://mlsanity.com/paper/2203.08034/) (2022)

## Abstract (arXiv)

Positron emission tomography (PET) seeks to balance diagnostic quality with ra-diation dose. Low-count PET noise is non-Gaussian, non-stationary, and spatial-ly dependent. It scales directly with local activity and is shaped by iterative recon-struction and physical corrections. Standard denoising diffusion probabilistic models (DDPMs) ignore these PET properties. Their forward process adds iso-tropic, homoscedastic Gaussian noise to the target. Such an approach fails to cap-ture the realistic physical degradation generated by the imaging system. To ad-dress the above limitations, this study introduces a heteroscedastic residual diffu-sion model (HDDPM) for low-count brain PET recovery in which the forward corruption is itself intensity-aware. We designed a fixed, Poisson-based variance module to generate voxel-wise noise maps. These maps naturally place stronger noise perturbation on low-activity regions than high-activity ones, meanwhile the network predicts the low-to-standard-count residual under explicit dose-fraction conditioning. We evaluated our proposed model (HDDPM) alongside generative frameworks across three different scanners, using both internal and external da-tasets at various simulated dose levels (1% to 50%). HDDPM and isotropic DDPM showed comparable overall image quality, but HDDPM stood out in the lowest-dose (1%) external scans. It is highly reliable and significantly reduces measurement errors in both high- and low-activity regions, compared to the standard model. These results support that heteroscedastic noising with the pro-posed HDDPM is feasible, and it provides a physically motivated inductive bias for quantitative low-count PET recovery by reflecting the activity-dependent noise structure of PET.