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Remarkable progress has been made within nonlinear Independent Component Analysis (ICA) and identifiable deep latent variable models. Formally, the latest nonlinear ICA theory enables us to recover the true latent variables up to a linear transformation by leveraging unsupervised deep learning. This is of significant importance for unsupervised learning in general as the true latent variables are of principal interest for meaningful representations. These theoretical results stand in stark contrast to the mostly heuristic approaches used for representation learning which do not provide analytical relations to the true latent variables. We extend the family of identifiable models by proposing an identifiable Variational Autoencoder (VAE) based Generative Adversarial Network (GAN) model we name iVAE-GAN. The latent space of most GANs, including VAE-GAN, is generally unrelated to the true latent variables. With iVAE-GAN we show the first principal approach to a theoretically meaningful latent space by means of adversarial training. We implement the novel iVAE-GAN architecture and show its identifiability, which is confirmed by experiments. The GAN objective is believed to be an important addition to identifiable models as it is one of the most powerful deep generative models. Furthermore, no requirements are imposed on the adversarial training leading to a very general model.

iVAE-GAN: Identifiable VAE-GAN Models for Latent Representation Learning