Aims. Highly resolved maps of the local Galactic dust are an important ingredient for sky emission models. Over almost the whole electromagnetic spectrum one can see imprints of dust, many of which originate from dust clouds within 300 pc. Having a detailed 3D reconstruction of these local dust clouds enables detailed studies, helps to quantify the impact on other observables, and is a necessary milestone of larger reconstructions, as every sightline for more distant objects will pass through the local dust. Methods. To infer the dust density we use parallax and extinction estimates published by the Gaia collaboration in their second data release (DR2). We model the dust as a log-normal process using a hierarchical Bayesian model. We also nonparametrically infer the kernel of the log-normal process, which corresponds to the physical spatial correlation power spectrum of the log-density. Results. Using only data from Gaia DR2, we reconstruct the 3D dust density and its spatial correlation spectrum in a 600 pc cube centered on the Sun. We report a spectral index of the logarithmic dust density of 3.1 on Fourier scales with wavelengths between 2 and 125 pc. The resulting 3D dust map as well as the power spectrum and posterior samples are publicly available for download.
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