Variational Autoencoders (VAEs) are a popular framework for unsupervised learning and data generation. A plethora of methods have been proposed focusing on improving VAEs, with the incorporation of adversarial objectives and the integration of prior learning mechanisms being prominent directions. When it comes to the former, an indicative instance is the recently introduced family of Introspective VAEs aiming at ensuring that a low likelihood is assigned to unrealistic samples. In this study, we focus on the Soft-IntroVAE (S-IntroVAE) and investigate the implication of incorporating a multimodal and learnable prior into this framework. Namely, we formulate the prior as a third player and show that when trained in cooperation with the decoder constitutes an effective way for prior learning, which shares the Nash Equilibrium with the vanilla S-IntroVAE. Furthermore, based on a modified formulation of the optimal ELBO in S-IntroVAE, we develop theoretically motivated regularizations, that is (i) adaptive variance clipping to stabilize training when learning the prior and (ii) responsibility regularization to discourage the formation of inactive prior mode. Finally, we perform a series of targeted experiments on a 2D density estimation benchmark and in an image generation setting comprised of the (F)-MNIST and CIFAR-10 datasets demonstrating the benefit of prior learning in S-IntroVAE in generation and representation learning.

The recently introduced introspective variational autoencoder (IntroVAE) exhibits outstanding image generations, and allows for amortized inference using an image encoder. The main idea in IntroVAE is to train a VAE adversarially, using the VAE encoder to discriminate between generated and real data samples. However, the original IntroVAE loss function relied on a particular hinge-loss formulation that is very hard to stabilize in practice, and its theoretical convergence analysis ignored important terms in the loss. In this work, we take a step towards better understanding of the IntroVAE model, its practical implementation, and its applications. We propose the Soft-IntroVAE, a modified IntroVAE that replaces the hinge-loss terms with a smooth exponential loss on generated samples. This change significantly improves training stability, and also enables theoretical analysis of the complete algorithm. Interestingly, we show that the IntroVAE converges to a distribution that minimizes a sum of KL distance from the data distribution and an entropy term. We discuss the implications of this result, and demonstrate that it induces competitive image generation and reconstruction. Finally, we describe two applications of Soft-IntroVAE to unsupervised image translation and out-of-distribution detection, and demonstrate compelling results. Code and additional information is available on the project website -- https://taldatech.github.io/soft-intro-vae-web