  Carbon monoxide (CO) is the best tracer of Galactic molecular hydrogen (H2).
Its lowest rotational emission lines are in the radio regime and thanks to
Galactic rotation emission at different distances is Doppler shifted. For a
given gas flow model the observed spectra can thus be deprojected along the
line of sight to infer the gas distribution. We use the CO line survey of Dame
et al. (2001) to reconstruct the three-dimensional density of H2. We consider
the deprojection as a Bayesian variational inference problem. The posterior
distribution of the gas densities allows us to estimate both the mean and
uncertainty of the reconstructed density. Unlike most of the previous attempts,
we take into account the correlations of gas on a variety of scales which
allows curing some of the well-known pathologies, like fingers-of-god effects.
Both gas flow models that we adopt incorporate a Galactic bar which induces
radial motions in the inner few kiloparsecs and thus offers spectral resolution
towards the Galactic centre. We compare our gas maps with those of earlier
studies and characterise their statistical properties, e.g. the radial profile
of the average surface mass density. We have made our three-dimensional gas
maps and their uncertainties available to the community at
https://dx.doi.org/10.5281/zenodo.4405437 .
