3D brain MRI generation has made significant advances in medical imaging, simulation, and controllable anatomical analysis. However, existing generative models typically synthesize 3D volumes monolithically, often overlooking regional anatomical structures and limiting local controllability. To address these limitations, we introduce AnaDiffusion, an anatomically compositional latent diffusion framework that factorizes the generation process into distinct, anatomically meaningful regions, followed by part-to-whole assembly and global refinement. Our approach first trains part diffusion models to capture local structural priors. We then inject an assembled anatomical composite of the parts into the whole-brain latent representation and continue denoising. This mechanism enables the model to resolve global context while preserving the injected anatomy. As a result, AnaDiffusion produces both explicit part assets and a globally coherent volume, thereby enabling controllable part editing without requiring subject-specific dense segmentation maps at inference time while maintaining consistent part-to-whole brain structure. On the subject-disjoint ADNI test split, AnaDiffusion achieves the lowest FID across the whole brain, left and right hemispheres, cerebellar-brainstem complex, and seam regions. It also achieves the best cerebellar and second-best ventricular and brainstem absolute Cohen's d values among the evaluated methods. In localized editing experiments, paired MS-SSIM demonstrates high target transfer and off-target preservation, supporting controllable part replacement with minimal unintended anatomical alterations.

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