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Generative adversarial networks (GANs) usually struggle in learning fromhighly diverse data, whose underlying manifold is complex. In this work, werevisit the mathematical foundations of GANs, and theoretically reveal that thenative adversarial loss for GAN training is insufficient to fix the problem ofsubsets with positive Lebesgue measure of the generated data manifold lying outof the real data manifold. Instead, we find that score matching serves as avalid solution to this issue thanks to its capability of persistently pushingthe generated data points towards the real data manifold. We thereby propose toimprove the optimization of GANs with score matching regularity (SMaRt).Regarding the empirical evidences, we first design a toy example to show thattraining GANs by the aid of a ground-truth score function can help reproducethe real data distribution more accurately, and then confirm that our approachcan consistently boost the synthesis performance of various state-of-the-artGANs on real-world datasets with pre-trained diffusion models acting as theapproximate score function. For instance, when training Aurora on the ImageNet64x64 dataset, we manage to improve FID from 8.87 to 7.11, on par with theperformance of one-step consistency model. The source code will be made public.

SMaRt: Improving GANs with Score Matching Regularity