On the Evaluation of Generative Models in Distributed Learning Tasks

The evaluation of deep generative models including generative adversarial networks (GANs) and diffusion models has been extensively studied in the literature. While the existing evaluation methods mainly target a centralized learning problem with training data stored by a single client, many applications of generative models concern distributed learning settings, e.g. the federated learning scenario, where training data are collected by and distributed among several clients. In this paper, we study the evaluation of generative models in distributed learning tasks with heterogeneous data distributions. First, we focus on the Fr\'echet inception distance (FID) and consider the following FID-based aggregate scores over the clients: 1) FID-avg as the mean of clients' individual FID scores, 2) FID-all as the FID distance of the trained model to the collective dataset containing all clients' data. We prove that the model rankings according to the FID-all and FID-avg scores could be inconsistent, which can lead to different optimal generative models according to the two aggregate scores. Next, we consider the kernel inception distance (KID) and similarly define the KID-avg and KID-all aggregations. Unlike the FID case, we prove that KID-all and KID-avg result in the same rankings of generative models. We perform several numerical experiments on standard image datasets and training schemes to support our theoretical findings on the evaluation of generative models in distributed learning problems.