Recently, generative adversarial networks (GANs) have achieved great impacts on a broad number of applications, including low resolution(LR) image synthesis. However, they suffer from unstable training especially when image resolution increases. To overcome this bottleneck, this paper generalizes the state-of-the-art Wasserstein GANs (WGANs) to an energy-relaxed objective which enables more stable and higher-resolution image generation. The benefits of this generalization can be summarized in three main points. Firstly, the proposed EnergyWGAN objective guarantees a valid symmetric divergence serving as a more rigorous and meaningful quantitative measure. Secondly, EnergyWGAN is capable of searching a more faithful solution space than the original WGANs without fixing a specific $k$-Lipschitz constraint. Finally, the proposed EnergyWGAN offers a natural way of stacking GANs for high resolution image generation. In our experiments we not only demonstrate the stable training ability of the proposed EnergyWGAN and its better image generation results on standard benchmark datasets, but also show the advantages over the state-of-the-art GANs on a real-world high resolution image dataset.

本文介绍一种新的Wasserstein距离(W-div)，并提出了基于此距离的生成对抗网络目标函数(WGAN-div)，该函数可以通过优化准确地近似W-div。实验结果表明，在标准图像合成基准测试中，WGAN-div具有比现有方法更优的性能和稳定性。

GAN的Wasserstein散度