Lack of early diagnosis often results in patients with Alzheimer progressing to irreversible mild to moderate cognitive impairment without timely treatment. The deposition of amyloid-beta (A beta) in the cerebral cortex, a definitive biomarker for Alzheimer's disease, is detectable through AV45 PET scans, facilitating early diagnosis of the condition. Clinically, accurate quantification of AV45 PET scans necessitate T1 images. However, the prevalent use of PET-CT over PET-MRI equipment entails additional MRI scans, leading to increased costs and patient burden. To address this clinical challenge, this paper proposes the structure-preserving denoising diffusion probabilistic model (SP-DDPM), capable of synthesizing the T1 images from AV45 PET scans. In the SP-DDPM, structural details from T1 images are incorporated into the diffusion model to emphasize anatomical accuracy. We also enhance the model's learning for the targeted brain areas using segmentation-based priors. Moreover, an exponential cosine noise strategy is proposed to improve the model's suitability for generating T1 images. In this study, we incorporated a large-scale cohort of 667 subjects from the ADNI and SILCODE databases to train and validate our models. The MR images generated from AV45 PET demonstrated similar signal patterns to real MR images. The average absolute error of the cortical composite region SUVR, estimated using our method, was 0.018 for the ADNI dataset and 0.041 for the SILCODE dataset, outperforming current techniques. The MR images generated by the SP-DDPM serve as an accurate template for amyloid quantification, facilitating precise AV45 PET scan quantification in the absence of real MR images. The application of this method is poised to streamline the diagnostic workflow for Alzheimer's disease, increase clinical work efficiency, and alleviate patient burden.