Background: Alzheimer's disease (AD) diagnosis heavily relies on amyloid-beta positron emission tomography (Abeta-PET), which is limited by high cost and limited accessibility. This study explores whether Abeta-PET spatial patterns can be predicted from blood-based biomarkers (BBMs) and MRI scans. Methods: We collected Abeta-PET images, T1-weighted MRI scans, and BBMs from 566 participants. A language-enhanced generative model, driven by a large language model (LLM) and multimodal information fusion, was developed to synthesize PET images. Synthesized images were evaluated for image quality, diagnostic consistency, and clinical applicability within a fully automated diagnostic pipeline. Findings: The synthetic PET images closely resemble real PET scans in both structural details (SSIM = 0.920 +/- 0.003) and regional patterns (Pearson's r = 0.955 +/- 0.007). Diagnostic outcomes using synthetic PET show high agreement with real PET-based diagnoses (accuracy = 0.80). Using synthetic PET, we developed a fully automatic AD diagnostic pipeline integrating PET synthesis and classification. The synthetic PET-based model (AUC = 0.78) outperforms T1-based (AUC = 0.68) and BBM-based (AUC = 0.73) models, while combining synthetic PET and BBMs further improved performance (AUC = 0.79). Ablation analysis supports the advantages of LLM integration and prompt engineering. Interpretation: Our language-enhanced generative model synthesizes realistic PET images, enhancing the utility of MRI and BBMs for Abeta spatial pattern assessment and improving the diagnostic workflow for Alzheimer's disease.