通过解耦医学影像内容与风格，实现跨中心3D影像合成与分析统一建模。

Self-supervised learning (SSL) and diffusion models have respectively advanced representation learning and generative modeling for high-dimensional 3D visual data, yet they are often developed as separate paradigms. Their unification remains challenging under multi-source heterogeneity, as anatomical content must be preserved for analysis while acquisition-related style varies across centers and affects synthesis. In this paper, we propose MeDUET, a 3D Medical image Disentangled UnifiEd PreTraining framework in the variational autoencoder latent space. MeDUET formulates unified pretraining as an empirical factor identifiability problem, aiming to learn domain-invariant content factors for anatomy and domain-specific style factors for appearance. To improve factor separation, MeDUET first uses token demixing with a standard adversarial domain regularizer to establish basic content-style specialization, and further introduces Mixed Factor Token Distillation and Swap-invariance Quadruplet Contrast to reduce mixed-region factor leakage and organize factor spaces with factor-wise invariance and discriminability. With these learned factors, MeDUET transfers effectively to both synthesis and analysis, yielding higher fidelity, faster convergence, and better controllability for synthesis, while achieving competitive or superior domain generalization and label efficiency on diverse datasets, tasks, and modalities. Overall, MeDUET shows that multi-source heterogeneity can serve as useful supervision, with disentanglement providing an effective interface for unifying 3D medical image synthesis and analysis. Our code is available at https://github.com/JK-Liu7/MeDUET.