  Allowing effective inference of latent vectors while training GANs can
greatly increase their applicability in various downstream tasks. Recent
approaches, such as ALI and BiGAN frameworks, develop methods of inference of
latent variables in GANs by adversarially training an image generator along
with an encoder to match two joint distributions of image and latent vector
pairs. We generalize these approaches to incorporate multiple layers of
feedback on reconstructions, self-supervision, and other forms of supervision
based on prior or learned knowledge about the desired solutions. We achieve
this by modifying the discriminator's objective to correctly identify more than
two joint distributions of tuples of an arbitrary number of random variables
consisting of images, latent vectors, and other variables generated through
auxiliary tasks, such as reconstruction and inpainting or as outputs of
suitable pre-trained models. We design a non-saturating maximization objective
for the generator-encoder pair and prove that the resulting adversarial game
corresponds to a global optimum that simultaneously matches all the
distributions. Within our proposed framework, we introduce a novel set of
techniques for providing self-supervised feedback to the model based on
properties, such as patch-level correspondence and cycle consistency of
reconstructions. Through comprehensive experiments, we demonstrate the
efficacy, scalability, and flexibility of the proposed approach for a variety
of tasks.
