Generative Adversarial Networks (GANs) are deep learning models that learn and generate new samples similar to existing ones. Traditionally, GANs are trained in centralized data centers, raising data privacy concerns due to the need for clients to upload their data. To address this, Federated Learning (FL) integrates with GANs, allowing collaborative training without sharing local data. However, this integration is complex because GANs involve two interdependent models—the generator and the discriminator—while FL typically handles a single model over distributed datasets. In this article, we propose a novel asynchronous FL framework for GANs, called AsyncFedGAN, designed to efficiently and distributively train both models tailored for molecule generation. AsyncFedGAN addresses the challenges of training interactive models, resolves the straggler issue in synchronous FL, reduces model staleness in asynchronous FL, and lowers client energy consumption. Our extensive simulations for molecular discovery show that AsyncFedGAN achieves convergence with proper settings, outperforms baseline methods, and balances model performance with client energy usage.