Alzheimer's disease (AD) is a progressive neurodegenerative disorder in which pathological changes begin many years before the onset of clinical symptoms, making early detection essential for timely intervention. T1-weighted (T1w) Magnetic Resonance Imaging (MRI) is routinely used in clinical practice to identify macroscopic brain alterations, but these changes typically emerge relatively late in the disease course. Diffusion MRI (dMRI), in contrast, is sensitive to earlier microstructural abnormalities by probing water diffusion in brain tissue. dMRI metrics, including fractional anisotropy (FA) and mean diffusivity (MD), provide complementary information about white matter integrity and neurodegeneration. However, dMRI acquisitions are time-consuming and susceptible to motion artifacts, limiting their routine use in clinical populations. To bridge this gap, I propose a 3D TransUNet image synthesis framework that predicts FA and MD maps directly from T1w MRI. My model generates high-fidelity maps, achieving a structural similarity index (SSIM) exceeding 0.93 and a strong Pearson correlation (>0.94) with ground-truth dMRI. When integrated into a multi-modal diagnostic model, these synthetic features boost AD classification accuracy by 5% (78.75%->83.75%) and, most importantly, improve mild cognitive impairment (MCI) detection by 12.5%. This study demonstrates that high-quality diffusion microstructural information can be inferred from routinely acquired T1w MRI, effectively transferring the benefits of multi-modality imaging to settings where diffusion data are unavailable. By reducing scan time while preserving complementary structural and microstructural information, the proposed approach has the potential to improve the accessibility, efficiency, and accuracy of AD diagnosis in clinical practice.