Generation/Synthesis of Data with CNNs

Question

Is it possible to use a trained CNN to generate data? After training on data of X and corresponding Ys, given a new Y to generate X? Or do I have to use GANs or RNNs? I'm still pretty new to the subject so I would be happy to have some leads, if I have to go in this direction.

Currently I am learning tensorflow and trying to implement the "Convolutional Sequence to Sequence Learning" paper

Clarification: I want to use a CNN to generate sequences of text. I have a reallyb big database of descriptions and also one of 1000 classes, and wanted to try it out with CNNs (since im coming from image classification)