  We present a non-parametric model for inferring the three-dimensional (3D)
distribution of dust density in the Milky Way. Our approach uses the extinction
measured towards stars at different locations in the Galaxy at approximately
known distances. Each extinction measurement is proportional to the integrated
dust density along its line-of-sight. Making simple assumptions about the
spatial correlation of the dust density, we can infer the most probable 3D
distribution of dust across the entire observed region, including along sight
lines which were not observed. This is possible because our model employs a
Gaussian Process to connect all lines-of-sight. We demonstrate the capability
of our model to capture detailed dust density variations using mock data as
well as simulated data from the Gaia Universe Model Snapshot. We then apply our
method to a sample of giant stars observed by APOGEE and Kepler to construct a
3D dust map over a small region of the Galaxy. Due to our smoothness constraint
and its isotropy, we provide one of the first maps which does not show the
"fingers of god" effect.
