Residual‑shifted diffusion model for efficient and accurate MRI‑based PET synthesis

Positron Emission Tomography (PET) is a medical imaging modality that provides important molecular and physiological information regarding cellular function and has the potential to be a valuable process in adaptive radiotherapy and cancer diagnosis. However, the clinical applications of PET imaging are limited by radiation exposure and widespread accessibility. Magnetic Resonance Imaging (MRI), by contrast, offers high-resolution anatomical information without radiation exposure, and is widely offered and accepted in clinical settings. Therefore, the development of MRI-to-PET synthesis frameworks is an increasingly relevant tool to enable broad clinical adoption and reduce radiation for PET imaging. Previous image synthesis models have shown promise but often introduce hallucinated features or require long inference times that hinder clinical integration. To address these limitations, we propose RES-PETDiff, a residual-shifted diffusion framework that synthesizes PET images from MRI inputs. Res-PETDiff uses residual differences to shift the PET and MRI domains during the forward diffusion process, allowing for the reverse diffusion process to be completed in as few as four steps. We demonstrate that Res-PETDiff outperforms leading baseline models (Pix2Pix, CycleGAN, and DDPM) through both qualitative and quantitative metrics. Res-PETDiff achieved a PSNR of 23.8dB and an SSIM of 0.827, outperforming Pix2Pix (21.7dB / 0.532), CycleGAN (20.8dB / 0.758), and DDPM (20.0dB / 0.601). It also obtained the lowest NMSE (0.070) and LPIPS (0.210) among all models. Furthermore, Res-PETDiff offered a 1,300× improvement in inference speed compared to standard DDPMs. This improvement in speed and accuracy signifies potential integration into clinical environments, enabling radiation-free synthetic PET imaging for treatments and broader oncological applications.