a noise distribution. The advantage of [**GAN**]{}s is the ability to generate clear samples with high perceptual quality. However, as described by Salimans [*et al.*]{} [@salimans2016improved], there are undesirable issues such as vanishing gradients and mode collapse in the training. The difficulties can be explained by the fact that minimizing the objective function for [**GAN**]{}s is equivalent to minimizing the Jensen-Shannon divergence, which is locally saturated and results in vanishing gradients, between the data and model distributions.

Later, Arjovsky [*et al.*]{} [@arjovsky2017wasserstein] addressed the gradient vanishing problem by introducing the weaker Wasserstain-1 distance $W(\mathbb{P}_r, \mathbb{P}_g)$ which gives clear gradients almost everywhere in the [**GAN**]{} model. The competition between the two networks is reformulated as our minimax optimization objective: $$\underset{G}{\min}  \underset{D \in \mathcal{D}}{\max}  \quad \underset{x  \sim \mathbb{P}_r} { \mathbb{E} } [ D(x)] - \underset{\tilde{x}  \sim \mathbb{P}_g} { \mathbb{E} } [ D(\tilde{x})]$$ where $\mathcal{D}$ is the set of $1$-Lipschitz functions such that ${\Vert D \Vert}_L \leq 1$. The original Lipschitz constraint enforcement proposed by Arjovsky at al. [@arjovsky2017wasserstein] is weight clipping to $[-c,c]$. Another approach proposed by Gulrajani [*et al.* ]{} [@gulrajani2017improved] is adding the gradient penality term $$\lambda \underset{\tilde{x}  \sim \mathbb{P}_{\tilde{x}}} { \mathbb{E} } [ {( {\Vert \nabla_{\tilde{x}} D(\tilde{x})\Vert}_2-1)}^2 ]$$ The 