The fusion of Federated Learning (FL) and deep generative models is transforming medical imaging by enabling privacy-preserving and data-efficient machine learning. Training large-scale deep models on radiological imaging data remains challenging due to data scarcity, heterogeneity, and strict privacy constraints that limit data sharing across institutions. FL addresses these challenges by employing collaborative model training that does not expose raw patient data, while generative models synthesize realistic medical images to alleviate scarcity and imbalance. The convergence of these two fields has given rise to federated generative models (FGMs), which extend Generative Adversarial Networks (GANs), Variational Autoencoders (VAE), and Diffusion models into distributed and privacy-preserving environments. FGMs have demonstrated significant potential in various medical imaging tasks, including data augmentation, image reconstruction, cross-modality conversion, and enhancing classification and segmentation models. Despite promising progress, the field remains in its early stages, facing open challenges in communication efficiency, scalability, data heterogeneity, and clinical reliability. This survey provides a comprehensive review of FGMs in medical imaging, analyzing their architectures, applications, and benchmark datasets, while highlighting key challenges and outlining future research directions to advance privacy-preserving generative modeling in healthcare.