Simulating prospective magnetic resonance imaging (MRI) scans from a given individual brain image is challenging, as it requires accounting for canonical changes in aging and/or disease progression while also considering the individual brain's current status and unique characteristics. While current deep generative models can produce high-resolution anatomically accurate templates for population-wide studies, their ability to predict future aging trajectories for individuals remains limited, particularly in capturing subject-specific neuroanatomical variations over time. In this study, we introduce Individualized Brain Synthesis (InBrainSyn), a framework for synthesizing high-resolution subject-specific longitudinal MRI scans that simulate neurodegeneration in both Alzheimer's disease (AD) and normal aging. InBrainSyn uses a parallel transport algorithm to adapt the population-level aging trajectories learned by a generative deep template network, enabling individualized aging synthesis. As InBrainSyn uses diffeomorphic transformations to simulate aging, the synthesized images are topologically consistent with the original anatomy by design. We evaluated InBrainSyn both quantitatively and qualitatively on AD and healthy control cohorts from the Open Access Series of Imaging Studies - version 3 dataset. Experimentally, InBrainSyn can also model neuroanatomical transitions between normal aging and AD. An evaluation of an external set supports its generalizability. Overall, with only a single baseline scan, InBrainSyn synthesizes realistic 3D spatiotemporal T1w MRI scans, producing personalized longitudinal aging trajectories. The code for InBrainSyn is available at https://github.com/Fjr9516/InBrainSyn.