Training robust learning algorithms across different medical imaging modalities is challenging due to the large domain gap. Unsupervised domain adaptation (UDA) mitigates this problem by using annotated images from the source domain and unlabeled images from the target domain to train the deep models. Existing approaches often rely on GAN-based style transfer, but these methods struggle to capture cross-domain mappings in regions with high variability. In this paper, we propose a unified framework, Bézier Meets Diffusion, for cross-domain image generation. First, we introduce a Bézier-curve-based style transfer strategy that effectively reduces the domain gap between source and target domains. The transferred source images enable the training of a more robust segmentation model across domains. Thereafter, using pseudo-labels generated by this segmentation model on the target domain, we train a conditional diffusion model (CDM) to synthesize high-quality, labeled target-domain images. To mitigate the impact of noisy pseudo-labels, we further develop an uncertainty-guided score matching method that improves the robustness of CDM training. Extensive experiments on public datasets demonstrate that our approach generates realistic labeled images, significantly augmenting the target domain and improving segmentation performance.