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Synthetic longitudinal brain MRI simulates brain aging and would enable more efficient research on neurodevelopmental and neurodegenerative conditions. Synthetically generated, age-adjusted brain images could serve as valuable alternatives to costly longitudinal imaging acquisitions, serve as internal controls for studies looking at the effects of environmental or therapeutic modifiers on brain development, and allow data augmentation for diverse populations. In this paper, we present a diffusion-based approach called SynthBrainGrow for synthetic brain aging with a two-year step. To validate the feasibility of using synthetically-generated data on downstream tasks, we compared structural volumetrics of two-year-aged brains against synthetically-aged brain MRI. Results show that SynthBrainGrow can accurately capture substructure volumetrics and simulate structural changes such as ventricle enlargement and cortical thinning. Our approach provides a novel way to generate longitudinal brain datasets from cross-sectional data to enable augmented training and benchmarking of computational tools for analyzing lifespan trajectories. This work signifies an important advance in generative modeling to synthesize realistic longitudinal data with limited lifelong MRI scans. The code is available at XXX.