Fast generation of 511 keV gamma volumetric phase space using a conditional diffusion model in carbon ion radiotherapy

Background and purpose Detecting 511 keV gamma rays is a promising approach for range estimation in carbon ion radiotherapy. However, due to the complexity of the reaction processes, Monte Carlo simulation speed of carbon ion interactions is extremely slow. This study aims to develop a fast and accurate generative model capable of reproducing the volumetric phase space of 511 keV gamma from specified input conditions to support Compton imaging application. Materials and methods A diffusion model was trained using Monte Carlo simulated 511 keV gamma characterized by six input conditions. The model was designed to generate volumetric phase space distributions conditioned on these parameters. The data generated were then used as the gamma source for a Compton camera, and its performance was evaluated by comparing the resulting distributions and reconstructed image with the reference Monte Carlo simulation. Results The diffusion model accurately generated the 511 keV gamma volumetric phase space for all six conditions. For most spatial and directional components, the relative error was within 2.5%, while a larger deviation (∼25%) was observed in the Bragg-peak region (PositionX). The PositionX distributions agreed well with the Monte Carlo simulations for most conditions; however, the largest discrepancy occurred for Condition 3, with differences of 15.0 mm and 18.0 mm at the 90% and 80% fall-off positions, respectively. The reconstructed Compton images also showed good agreement. For Condition 0, the 1D profile exhibited a peak-position difference of 2.0 mm, with differences of 0.5 mm and 2.2 mm at the 90% and 80% fall-off positions, respectively. Conclusions The proposed diffusion model enables rapid and accurate generation of 511 keV gamma volumetric phase space data from defined input conditions, greatly reducing dependence on slow Monte Carlo simulations. It offers a practical and efficient tool for Compton imaging within carbon ion radiotherapy workflow.