  A large part of the literature on learning disentangled representations
focuses on variational autoencoders (VAE). Recent developments demonstrate that
disentanglement cannot be obtained in a fully unsupervised setting without
inductive biases on models and data. However, Khemakhem et al., AISTATS, 2020
suggest that employing a particular form of factorized prior, conditionally
dependent on auxiliary variables complementing input observations, can be one
such bias, resulting in an identifiable model with guarantees on
disentanglement. Working along this line, we propose a novel VAE-based
generative model with theoretical guarantees on identifiability. We obtain our
conditional prior over the latents by learning an optimal representation, which
imposes an additional strength on their regularization. We also extend our
method to semi-supervised settings. Experimental results indicate superior
performance with respect to state-of-the-art approaches, according to several
established metrics proposed in the literature on disentanglement.
