Title: Training Federated GANs  with Theoretical Guarantees: A Universal Aggregation Approach. Abstract: Recently, Generative Adversarial Networks (GANs) have demonstrated their potential in federated learning, i.e., learning a centralized model from data privately hosted by multiple sites. A federated GAN jointly trains a centralized generator and multiple private discriminators hosted at different sites. A major theoretical challenge for the federated GAN is the heterogeneity of the local data distributions. Traditional approaches cannot guarantee to learn the target distribution, which is a mixture of the highly different local distributions. This paper tackles this theoretical challenge, and for the first time, provides a provably correct framework for federated GAN. We propose a new approach called Universal Aggregation, which simulates a centralized discriminator via carefully aggregating the mixture of all private discriminators. We prove that a generator trained with this simulated centralized discriminator can learn the desired target distribution. Through synthetic and real datasets, we show that our method can learn the mixture of largely different distributions, when existing federated GAN methods fail to.