Generative adversarial networks (GANs) usually struggle in learning from highly diverse data, whose underlying manifold is complex. In this work, we revisit the mathematical foundations of GANs, and theoretically reveal that the native adversarial loss for GAN training is insufficient to fix the problem of subsets with positive Lebesgue measure of the generated data manifold lying out of the real data manifold. Instead, we find that score matching serves as a valid solution to this issue thanks to its capability of persistently pushing the generated data points towards the real data manifold. We thereby propose to improve the optimization of GANs with score matching regularity (SMaRt). Regarding the empirical evidences, we first design a toy example to show that training GANs by the aid of a ground-truth score function can help reproduce the real data distribution more accurately, and then confirm that our approach can consistently boost the synthesis performance of various state-of-the-art GANs on real-world datasets with pre-trained diffusion models acting as the approximate score function. For instance, when training Aurora on the ImageNet 64x64 dataset, we manage to improve FID from 8.87 to 7.11, on par with the performance of one-step consistency model. The source code will be made public.

生成对抗网络（GAN）的数学基础不足以解决复杂多样数据的学习问题，通过引入分数匹配（score matching）的正则化优化方法（SMaRt），在各种现实世界数据集上提高了各种最新GAN的综合性能。

SMaRt：基于分数匹配规则改进GANs