  Separating high-dimensional data like images into independent latent factors,
i.e independent component analysis (ICA), remains an open research problem. As
we show, existing probabilistic deep generative models (DGMs), which are
tailor-made for image data, underperform on non-linear ICA tasks. To address
this, we propose a DGM which combines bijective feature maps with a linear ICA
model to learn interpretable latent structures for high-dimensional data. Given
the complexities of jointly training such a hybrid model, we introduce novel
theory that constrains linear ICA to lie close to the manifold of orthogonal
rectangular matrices, the Stiefel manifold. By doing so we create models that
converge quickly, are easy to train, and achieve better unsupervised latent
factor discovery than flow-based models, linear ICA, and Variational
Autoencoders on images.
