  MRI and CT are most widely used medical imaging modalities. It is often
necessary to acquire multi-modality images for diagnosis and treatment such as
radiotherapy planning. However, multi-modality imaging is not only costly but
also introduces misalignment between MRI and CT images. To address this
challenge, computational conversion is a viable approach between MRI and CT
images, especially from MRI to CT images. In this paper, we propose to use an
emerging deep learning framework called diffusion and score-matching models in
this context. Specifically, we adapt denoising diffusion probabilistic and
score-matching models, use four different sampling strategies, and compare
their performance metrics with that using a convolutional neural network and a
generative adversarial network model. Our results show that the diffusion and
score-matching models generate better synthetic CT images than the CNN and GAN
models. Furthermore, we investigate the uncertainties associated with the
diffusion and score-matching networks using the Monte-Carlo method, and improve
the results by averaging their Monte-Carlo outputs. Our study suggests that
diffusion and score-matching models are powerful to generate high quality
images conditioned on an image obtained using a complementary imaging modality,
analytically rigorous with clear explainability, and highly competitive with
CNNs and GANs for image synthesis.
