Investigating the reasons behind the accelerated expansion of the universe is one of the main challenges in astronomy and modern cosmology. Future space missions, such as Euclid, will provide images of billions of galaxies in order to investigate the so-called dark matter and probe the geometry of the universe. Due to the very large-scale data provided by such missions, automated algorithms are needed for measurement and detection purposes. The training and calibration of such algorithms require simulated, or synthetic, images of galaxies that mimic the real observations and exhibit real morphologies. 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-based methods used in astronomical data processing.