The traditional role of the network layer is the transfer of packet replicas from source to destination through intermediate network nodes. We present a generative network layer that uses Generative AI (GenAI) at intermediate or edge network nodes and analyze its impact on the required data rates in the network. We conduct a case study where the GenAI-aided nodes generate images from prompts that consist of substantially compressed latent representations. The results from network flow analyses under image quality constraints show that the generative network layer can achieve an improvement of more than 100% in terms of the required data rate.