Accurately modeling longitudinal brain MRI progression is crucial for understanding neurodegenerative diseases and predicting individualized structural changes. Existing state-of-the-art approaches, such as Brain Latent Progression (BrLP), often use multi-stage training pipelines with auxiliary conditioning modules but suffer from architectural complexity, suboptimal use of conditional clinical covariates, and limited guarantees of anatomical consistency. We propose Anatomically Guided Latent Diffusion Model (AG-LDM), a segmentation-guided framework that enforces anatomically consistent progression while substantially simplifying the training pipeline. AG-LDM conditions latent diffusion by directly fusing baseline anatomy, noisy follow-up states, and clinical covariates at the input level, a strategy that avoids auxiliary control networks by learning a unified, end-to-end model that represents both anatomy and progression. A lightweight 3D tissue segmentation model (WarpSeg) provides explicit anatomical supervision during both autoencoder fine-tuning and diffusion model training, ensuring consistent brain tissue boundaries and morphometric fidelity. Experiments on 31,713 ADNI longitudinal pairs and zero-shot evaluation on OASIS-3 demonstrate that AG-LDM matches or surpasses more complex diffusion models, achieving state-of-the-art image quality and 15-20\% reduction in volumetric errors in generated images. AG-LDM also exhibits markedly stronger utilization of temporal and clinical covariates (up to 31.5x higher sensitivity than BrLP) and generates biologically plausible counterfactual trajectories, accurately capturing hallmarks of Alzheimer's progression such as limbic atrophy and ventricular expansion. These results highlight AG-LDM as an efficient, anatomically grounded framework for reliable brain MRI progression modeling.