  We present a machine learning approach using normalising flows for inferring
cosmological parameters from gravitational wave events. Our methodology is
general to any type of compact binary coalescence event and cosmological model
and relies on the generation of training data representing distributions of
gravitational wave event parameters. These parameters are conditional on the
underlying cosmology and incorporate prior information from galaxy catalogues.
We provide an example analysis inferring the Hubble constant using binary black
holes detected during the O1, O2, and O3 observational runs conducted by the
advanced LIGO/VIRGO gravitational wave detectors. We obtain a Bayesian
posterior on the Hubble constant from which we derive an estimate and 1$\sigma$
confidence bounds of $H_{0} = 74.51^{+14.80}_{-13.63} \: \text{km}
\:\text{s}^{-1} \text{Mpc}^{-1}$. We are able to compute this result in
$\mathcal{O}(1)$ s using our trained Normalising Flow model.
