  Generative Adversarial Networks (GANs) have been widely adopted in various
fields. However, existing GANs generally are not able to preserve the manifold
of data space, mainly due to the simple representation of discriminator for the
real/generated data. To address such open challenges, this paper proposes
Manifold-preserved GANs (MaF-GANs), which generalize Wasserstein GANs into
high-dimensional form. Specifically, to improve the representation of data, the
discriminator in MaF-GANs is designed to map data into a high-dimensional
manifold. Furthermore, to stabilize the training of MaF-GANs, an operation with
precise and universal solution for any K-Lipschitz continuity, called
Topological Consistency is proposed. The effectiveness of the proposed method
is justified by both theoretical analysis and empirical results. When adopting
DCGAN as the backbone on CelebA (256*256), the proposed method achieved 12.43
FID, which outperforms the state-of-the-art model like Realness GAN (23.51 FID)
by a large margin. Code will be made publicly available.
