  In this paper we introduce a new structure to Generative Adversarial Networks
by adding an inverse transformation unit behind the generator. We present two
theorems to claim the convergence of the model, and two conjectures to nonideal
situations when the transformation is not bijection. A general survey on models
with different transformations was done on the MNIST dataset and the
Fashion-MNIST dataset, which shows the transformation does not necessarily need
to be bijection. Also, with certain transformations that blurs an image, our
model successfully learned to sharpen the images and recover blurred images,
which was additionally verified by our measurement of sharpness.
