Contrastive Analysis (CA) deals with the discovery of what is common and what is distinctive of a target domain compared to a background one. This is of great interest in many applications, such as medical imaging. Current state-of-the-art (SOTA) methods are latent variable models based on VAE (CA-VAEs). However, they all either ignore important constraints or they don't enforce fundamental assumptions. This may lead to sub-optimal solutions where distinctive factors are mistaken for common ones (or viceversa). Furthermore, the generated images have a rather poor quality, typical of VAEs, decreasing their interpretability and usefulness. Here, we propose Double InfoGAN, the first GAN based method for CA that leverages the high-quality synthesis of GAN and the separation power of InfoGAN. Experimental results on four visual datasets, from simple synthetic examples to complex medical images, show that the proposed method outperforms SOTA CA-VAEs in terms of latent separation and image quality. Datasets and code are available online.