Generative models trained on multi-institutional datasets can provide an enriched understanding through diverse data distributions. However, training the models on medical images is often challenging due to hospitals' reluctance to share data for privacy reasons. Federated learning(FL) has emerged as a privacy-preserving solution for training distributed datasets across data centers by aggregating model weights from multiple clients instead of sharing raw data. Previous research has explored the adaptation of FL to generative models, yet effective aggregation algorithms specifically tailored for generative models remain unexplored. We hereby propose a novel algorithm aimed at improving the performance of generative models within FL. Our approach adaptively re-weights the contribution of each client, resulting in well-trained shared parameters. In each round, the server side measures the distribution distance between fake images generated by clients instead of directly comparing the Fréchet Inception Distance per client, thereby enhancing efficiency of the learning. Experimental results on three public chest X-ray datasets show superior performance in medical image generation, outperforming both centralized learning and conventional FL algorithms. Our code is available at https://github.com/danny0628/FedCAR.