  MRI and PET are crucial diagnostic tools for brain diseases, as they provide
complementary information on brain structure and function. However, PET
scanning is costly and involves radioactive exposure, resulting in a lack of
PET. Moreover, simultaneous PET and MRI at ultra-high-field are currently
hardly infeasible. Ultra-high-field imaging has unquestionably proven valuable
in both clinical and academic settings, especially in the field of cognitive
neuroimaging. These motivate us to propose a method for synthetic PET from
high-filed MRI and ultra-high-field MRI. From a statistical perspective, the
joint probability distribution (JPD) is the most direct and fundamental means
of portraying the correlation between PET and MRI. This paper proposes a novel
joint diffusion attention model which has the joint probability distribution
and attention strategy, named JDAM. JDAM has a diffusion process and a sampling
process. The diffusion process involves the gradual diffusion of PET to
Gaussian noise by adding Gaussian noise, while MRI remains fixed. JPD of MRI
and noise-added PET was learned in the diffusion process. The sampling process
is a predictor-corrector. PET images were generated from MRI by JPD of MRI and
noise-added PET. The predictor is a reverse diffusion process and the corrector
is Langevin dynamics. Experimental results on the public Alzheimer's Disease
Neuroimaging Initiative (ADNI) dataset demonstrate that the proposed method
outperforms state-of-the-art CycleGAN for high-field MRI (3T MRI). Finally,
synthetic PET images from the ultra-high-field (5T MRI and 7T MRI) be
attempted, providing a possibility for ultra-high-field PET-MRI imaging.
