We introduce a new architecture called a conditional invertible neural\nnetwork (cINN), and use it to address the task of diverse image-to-image\ntranslation for natural images. This is not easily possible with existing INN\nmodels due to some fundamental limitations. The cINN combines the purely\ngenerative INN model with an unconstrained feed-forward network, which\nefficiently preprocesses the conditioning image into maximally informative\nfeatures. All parameters of a cINN are jointly optimized with a stable, maximum\nlikelihood-based training procedure. Even though INN-based models have received\nfar less attention in the literature than GANs, they have been shown to have\nsome remarkable properties absent in GANs, e.g. apparent immunity to mode\ncollapse. We find that our cINNs leverage these properties for image-to-image\ntranslation, demonstrated on day to night translation and image colorization.\nFurthermore, we take advantage of our bidirectional cINN architecture to\nexplore and manipulate emergent properties of the latent space, such as\nchanging the image style in an intuitive way.\n