  We address the problem of unsupervised disentanglement of latent
representations learnt via deep generative models. In contrast to current
approaches that operate on the evidence lower bound (ELBO), we argue that
statistical independence in the latent space of VAEs can be enforced in a
principled hierarchical Bayesian manner. To this effect, we augment the
standard VAE with an inverse-Wishart (IW) prior on the covariance matrix of the
latent code. By tuning the IW parameters, we are able to encourage (or
discourage) independence in the learnt latent dimensions. Extensive
experimental results on a range of datasets (2DShapes, 3DChairs, 3DFaces and
CelebA) show our approach to outperform the $\beta$-VAE and is competitive with
the state-of-the-art FactorVAE. Our approach achieves significantly better
disentanglement and reconstruction on a new dataset (CorrelatedEllipses) which
introduces correlations between the factors of variation.
