  One major drawback of state-of-the-art artificial intelligence is its lack of
explainability. One approach to solve the problem is taking causality into
account. Causal mechanisms can be described by structural causal models. In
this work, we propose a method for estimating bivariate structural causal
models using a combination of normalising flows applied to density estimation
and variational Gaussian process regression for post-nonlinear models. It
facilitates causal discovery, i.e. distinguishing cause and effect, by either
the independence of cause and residual or a likelihood ratio test. Our method
which estimates post-nonlinear models can better explain a variety of
real-world cause-effect pairs than a simple additive noise model. Though it
remains difficult to exploit this benefit regarding all pairs from the
T\"ubingen benchmark database, we demonstrate that combining the additive noise
model approach with our method significantly enhances causal discovery.
