tract: Natural images can be regarded as residing in a manifold that is embedded in a higher dimensional Euclidean space. Generative Adversarial Networks (GANs) try to learn the distribution of the real images in the manifold to generate samples that look real. But the results of existing methods still exhibit many unpleasant artifacts and distortions even for the cases where the desired ground truth target images are available for supervised learning such as in single image super resolution (SISR). We probe for ways to alleviate these problems for supervised GANs in this paper. We explicitly apply the Lipschitz Continuity Condition (LCC) to regularize the GAN. An encoding network that maps the image space to a new optimal latent space is derived from the LCC, and it is used to augment the GAN as a coupling component. The LCC is also converted to new regularization terms in the generator loss function to enforce local invariance. The GAN is optimized together with the encoding network in an attempt to make the generator converge to a more ideal and disentangled mapping that can generate samples more faithful to the target images. When the proposed models are applied to the single image super resolution problem, the results outperform the state of the art.