We present a method for simultaneously learning, in an unsupervised manner, (i) a conditional image generator, (ii) foreground extraction and segmentation, (iii) clustering into a two-level class hierarchy, and (iv) object removal and background completion, all done without any use of annotation. The method combines a Generative Adversarial Network and a Variational Auto-Encoder, with multiple encoders, generators and discriminators, and benefits from solving all tasks at once. The input to the training scheme is a varied collection of unlabeled images from the same domain, as well as a set of background images without a foreground object. In addition, the image generator can mix the background from one image, with a foreground that is conditioned either on that of a second image or on the index of a desired cluster. The method obtains state of the art results in comparison to the literature methods, when compared to the current state of the art in each of the tasks.