Cerebral small vessel disease is the most common pathology underlying vascular dementia. In small vessel disease, diffusion tensor imaging is more sensitive to white matter damage and better predicts dementia risk than conventional magnetic resonance imaging sequences, such as T1 and fluid attenuation inversion recovery, but diffusion tensor imaging takes longer to acquire and is not routinely available in clinical practice. As diffusion tensor imaging-derived scalar maps-fractional anisotropy (FA) and mean diffusivity (MD)-are frequently used in clinical settings, one solution is to synthesize FA/MD from T1 images. We developed a deep learning model to synthesize FA/MD from T1. The training data set consisted of 4998 participants with the highest white matter hyperintensity volumes in the UK Biobank. Four external validations data sets with small vessel disease were included: SCANS (St George's Cognition and Neuroimaging in Stroke; n=120), RUN DMC (Radboud University Nijmegen Diffusion Tensor and Magnetic Resonance Imaging Cohort; n=502), PRESERVE (Blood Pressure in Established Cerebral Small Vessel Disease; n=105), and NETWORKS (n=26), along with 1000 normal controls from the UK Biobank. The synthetic maps resembled ground-truth maps (structural similarity index >0.89 for MD maps and >0.80 for FA maps across all external validation data sets except for SCANS). The prediction accuracy of dementia using whole-brain median MD from the synthetic maps is comparable to the ground truth (SCANS ground-truth c-index, 0.822 and synthetic, 0.821; RUN DMC ground truth, 0.816 and synthetic, 0.812) and better than white matter hyperintensity volume (SCANS, 0.534; RUN DMC, 0.710). We have developed a fast and generalizable method to synthesize FA/MD maps from T1 to improve the prediction accuracy of dementia in small vessel disease when diffusion tensor imaging data have not been acquired.