Generative adversarial networks (GANs) learn a target probability distribution by optimizing a generator and a discriminator with minimax objectives. This paper addresses the question of whether such optimization actually provides the generator with gradients that make its distribution close to the target distribution. We derive metrizable conditions, sufficient conditions for the discriminator to serve as the distance between the distributions by connecting the GAN formulation with the concept of sliced optimal transport. Furthermore, by leveraging these theoretical results, we propose a novel GAN training scheme, called slicing adversarial network (SAN). With only simple modifications, a broad class of existing GANs can be converted to SANs. Experiments on synthetic and image datasets support our theoretical results and the SAN's effectiveness as compared to usual GANs. Furthermore, we also apply SAN to StyleGAN-XL, which leads to state-of-the-art FID score amongst GANs for class conditional generation on ImageNet 256$\times$256.

翻译：生成对抗网络（GAN）通过极小极大目标优化生成器与判别器来学习目标概率分布。本文探讨此类优化是否能真正为生成器提供使其分布逼近目标分布的梯度。通过将GAN框架与切片最优传输概念相结合，我们推导出可度量性条件——即判别器作为分布间距离度量函数的充分条件。进一步，基于这些理论成果，我们提出一种新型GAN训练方案，称为切片对抗网络（SAN）。仅需简单修改，现有广泛类别的GAN即可转换为SAN。在合成数据集与图像数据集上的实验验证了我们的理论结果，并表明SAN相较于常规GAN的有效性。此外，我们将SAN应用于StyleGAN-XL，在ImageNet 256×256条件类别生成任务中，取得了GAN领域最优的FID分数。