In this work, we provide an efficient and realistic data-driven approach to simulate astronomical images using deep generative models from machine learning. Our solution is based on a variant of the generative adversarial network (GAN) with progressive training methodology and Wasserstein cost function. The proposed solution generates naturalistic images of galaxies that show complex structures and high diversity, which suggests that data-driven simulations using machine learning can replace many of the expensive model-driven methods used in astronomical data processing.