Recent advancements in generative learning have enabled PET image synthesis from relatively more accessible MRI scans, offering a safer, cost-effective, and scalable alternative to traditional PET imaging, e.g., for Alzheimer’s disease (AD) diagnosis. However, current MRI-to-PET translation methods face limitations in controllability and fidelity, often failing to capture personalized metabolic activations and fine-grained structural details in critical regions. To address these challenges, we propose a novel controllable MRI-to-PET translation framework, termed DIReCT, which leverages rectified flow to generate high-fidelity PET images tailored to downstream diagnostic and analytical needs. By injecting cross-modal guidance from a pretrained vision-language model (BiomedCLIP), DIReCT incorporates both common imaging knowledge and individualized clinical information to enhance the personalization of PET synthesis. Extensive experiments on the ADNI dataset demonstrate that DIReCT significantly outperforms existing methods across various image quality metrics. Notably, the synthesized FDG-PET images by DIReCT achieve analytical performance comparable to real FDG-PET scans, excelling in capturing AD-related pathological features for reliable group comparisons and personalized diagnosis.