  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 $\textit{in-silico}$ 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.
