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.

分布式学习任务中生成模型的评估方法主要关注深度生成模型、评估方法、分布式学习、Fréchet inception distance 和 kernel inception distance。