The global population is aging rapidly, and aging is a major risk factor for various diseases. It is an important task to predict how each individual's brain will age, as the brain supports many human functions. This capability can greatly facilitate healthcare automation by enabling personalized, proactive intervention and efficient healthcare resource allocation. However, this task is extremely challenging because of the brain's complex 3D anatomy. While there have been successes in natural image generation and brain MRI synthesis, existing methods fall short in generating individualized, anatomically faithful aging brain trajectories. To address these gaps, we propose BrainPath, a novel AI model that, given a single structural MRI of an individual, generates synthetic longitudinal MRIs that represent that individual's expected brain anatomy as they age. BrainPath introduces three architectural innovations: an age-aware encoder with biologically grounded supervision, a differential age conditioned decoder for anatomically faithful MRI synthesis, and a swap-learning strategy that implicitly separates stable subject-specific anatomy from aging effects. We further design biologically informed loss functions, including an age calibration loss and an age and structural perceptual loss, to complement the conventional reconstruction loss. This enables the model to capture subtle, temporally meaningful anatomical changes associated with aging. We apply BrainPath to two of the largest public aging datasets and conduct a comprehensive, multifaceted evaluation. Our results demonstrate BrainPath's superior performance in generation accuracy, anatomical fidelity, and cross-dataset generalizability, outperforming competing methods.