The scarcity and complexity of voxel-level annotations in 3D medical imaging present significant challenges, particularly due to the domain gap between labeled datasets from well-resourced centers and unlabeled datasets from less-resourced centers. This disparity affects the fairness of artificial intelligence algorithms in healthcare. We introduce Diffuse-UDA, a novel method leveraging diffusion models to tackle Unsupervised Domain Adaptation (UDA) in medical image segmentation. Diffuse-UDA generates high-quality image-mask pairs with target domain characteristics and various structures, thereby enhancing UDA tasks. Initially, pseudo labels for target domain samples are generated. Subsequently, a specially tailored diffusion model, incorporating deformable augmentations, is trained on image-label or image-pseudo-label pairs from both domains. Finally, source domain labels guide the diffusion model to generate image-label pairs for the target domain. Comprehensive evaluations on several benchmarks demonstrate that Diffuse-UDA outperforms leading UDA and semi-supervised strategies, achieving performance close to or even surpassing the theoretical upper bound of models trained directly on target domain data. Diffuse-UDA offers a pathway to advance the development and deployment of AI systems in medical imaging, addressing disparities between healthcare environments. This approach enables the exploration of innovative AI-driven diagnostic tools, improves outcomes, saves time, and reduces human error.