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Knowing the Galactic 3D dust distribution is relevant for understanding manyprocesses in the interstellar medium and for correcting many astronomicalobservations for dust absorption and emission. Here, we aim for a 3Dreconstruction of the Galactic dust distribution with an increase in the numberof meaningful resolution elements by orders of magnitude with respect toprevious reconstructions, while taking advantage of the dust's spatialcorrelations to inform the dust map. We use iterative grid refinement to definea log-normal process in spherical coordinates. This log-normal process assumesa fixed correlation structure, which was inferred in an earlier reconstructionof Galactic dust. Our map is informed through 111 Million data points,combining data of PANSTARRS, 2MASS, Gaia DR2 and ALLWISE. The log-normalprocess is discretized to 122 Billion degrees of freedom, a factor of 400 morethan our previous map. We derive the most probable posterior map and anuncertainty estimate using natural gradient descent and the Fisher-Laplaceapproximation. The dust reconstruction covers a quarter of the volume of ourGalaxy, with a maximum coordinate distance of $16\,\text{kpc}$, and meaningfulinformation can be found up to at distances of $4\,$kpc, still improving uponour earlier map by a factor of 5 in maximal distance, of $900$ in volume, andof about eighteen in angular grid resolution. Unfortunately, the maximumposterior approach chosen to make the reconstruction computational affordableintroduces artifacts and reduces the accuracy of our uncertainty estimate.Despite of the apparent limitations of the presented 3D dust map, a good partof the reconstructed structures are confirmed by independent maserobservations. Thus, the map is a step towards reliable 3D Galactic cartographyand already can serve for a number of tasks, if used with care.

The Galactic 3D large-scale dust distribution via Gaussian process regression on spherical coordinates