  Knowing the Galactic 3D dust distribution is relevant for understanding many
processes in the interstellar medium and for correcting many astronomical
observations for dust absorption and emission. Here, we aim for a 3D
reconstruction of the Galactic dust distribution with an increase in the number
of meaningful resolution elements by orders of magnitude with respect to
previous reconstructions, while taking advantage of the dust's spatial
correlations to inform the dust map. We use iterative grid refinement to define
a log-normal process in spherical coordinates. This log-normal process assumes
a fixed correlation structure, which was inferred in an earlier reconstruction
of Galactic dust. Our map is informed through 111 Million data points,
combining data of PANSTARRS, 2MASS, Gaia DR2 and ALLWISE. The log-normal
process is discretized to 122 Billion degrees of freedom, a factor of 400 more
than our previous map. We derive the most probable posterior map and an
uncertainty estimate using natural gradient descent and the Fisher-Laplace
approximation. The dust reconstruction covers a quarter of the volume of our
Galaxy, with a maximum coordinate distance of $16\,\text{kpc}$, and meaningful
information can be found up to at distances of $4\,$kpc, still improving upon
our earlier map by a factor of 5 in maximal distance, of $900$ in volume, and
of about eighteen in angular grid resolution. Unfortunately, the maximum
posterior approach chosen to make the reconstruction computational affordable
introduces artifacts and reduces the accuracy of our uncertainty estimate.
Despite of the apparent limitations of the presented 3D dust map, a good part
of the reconstructed structures are confirmed by independent maser
observations. Thus, the map is a step towards reliable 3D Galactic cartography
and already can serve for a number of tasks, if used with care.
