Predicting future brain state from a baseline magnetic resonance image (MRI) is a central challenge in neuroimaging and has important implications for studying neurodegenerative diseases such as Alzheimer's disease (AD). Most existing approaches predict future cognitive scores or clinical outcomes, such as conversion from mild cognitive impairment to dementia. Instead, here we investigate longitudinal MRI image-to-image prediction that forecasts a participant's entire brain MRI several years into the future, intrinsically modeling complex, spatially distributed neurodegenerative patterns. We implement and evaluate five deep learning architectures (UNet, U2-Net, UNETR, Time-Embedding UNet, and ODE-UNet) on two longitudinal cohorts (ADNI and AIBL). Predicted follow-up MRIs are directly compared with the actual follow-up scans using metrics that capture global similarity and local differences. The best performing models achieve high-fidelity predictions, and all models generalize well to an independent external dataset, demonstrating robust cross-cohort performance. Our results indicate that deep learning can reliably predict participant-specific brain MRI at the voxel level, offering new opportunities for individualized prognosis.