  Magnetic resonance imaging (MRI) and positron emission tomography (PET) are
increasingly used in multimodal analysis of neurodegenerative disorders. While
MRI is broadly utilized in clinical settings, PET is less accessible. Many
studies have attempted to use deep generative models to synthesize PET from MRI
scans. However, they often suffer from unstable training and inadequately
preserve brain functional information conveyed by PET. To this end, we propose
a functional imaging constrained diffusion (FICD) framework for 3D brain PET
image synthesis with paired structural MRI as input condition, through a new
constrained diffusion model (CDM). The FICD introduces noise to PET and then
progressively removes it with CDM, ensuring high output fidelity throughout a
stable training phase. The CDM learns to predict denoised PET with a functional
imaging constraint introduced to ensure voxel-wise alignment between each
denoised PET and its ground truth. Quantitative and qualitative analyses
conducted on 293 subjects with paired T1-weighted MRI and
18F-fluorodeoxyglucose (FDG)-PET scans suggest that FICD achieves superior
performance in generating FDG-PET data compared to state-of-the-art methods. We
further validate the effectiveness of the proposed FICD on data from a total of
1,262 subjects through three downstream tasks, with experimental results
suggesting its utility and generalizability.
