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Context. High-resolution 3D maps of interstellar dust are critical for probing the underlying physics shaping the structure of the interstellar medium, and for foreground correction of astrophysical observations affected by dust. Aims. We aim to construct a new 3D map of the spatial distribution of interstellar dust extinction out to a distance of 1.25 kpc from the Sun. Methods. We leveraged distance and extinction estimates to 54 million nearby stars derived from the Gaia BP/RP spectra. Using the stellar distance and extinction information, we inferred the spatial distribution of dust extinction. We modeled the logarithmic dust extinction with a Gaussian process in a spherical coordinate system via iterative charted refinement and a correlation kernel inferred in previous work. In total, our posterior has over 661 million degrees of freedom. We probed the posterior distribution using the variational inference method MGVI. Results. Our 3D dust map has an angular resolution of up to 14′ ( N side = 256), and we achieve parsec-scale distance resolution, sampling the dust in 516 logarithmically spaced distance bins spanning 69 pc to 1250 pc. We generated 12 samples from the variational posterior of the 3D dust distribution and release the samples alongside the mean 3D dust map and its corresponding uncertainty. Conclusions. Our map resolves the internal structure of hundreds of molecular clouds in the solar neighborhood and will be broadly useful for studies of star formation, Galactic structure, and young stellar populations. It is available for download in a variety of coordinate systems online and can also be queried via the publicly available dustmaps Python package.