Export of sinking particles from the surface ocean is critical for carbon sequestration and to provide energy to the deep biosphere. The magnitude and spatial patterns of this export have been estimated in the past by \emph{in situ} particle flux observations, satellite-based algorithms, and ocean biogeochemical models; however, these estimates remain uncertain. Here, we use a recent machine learning reconstruction of global ocean particle size distributions from Underwater Vision Profiler 5 (UVP5) measurements to estimate carbon fluxes by sinking particles (35 $\mu$m - 5 mm equivalent spherical diameter) from the surface ocean. We combine global maps of particle size distribution properties with empirical relationships constrained against \emph{in situ} flux observations to calculate particulate carbon export from the euphotic zone and wintertime mixed layer depths. The new flux reconstructions suggest a less variable seasonal cycle in the tropical ocean, and a more persistent export in the Southern Ocean than previously recognized. Smaller particles (less than 420 $\mu$m) contribute most of the flux globally, while larger particles become more important at high latitudes and in tropical upwelling regions. Export from the wintertime mixed layer globally exceeds that from the euphotic zone, suggesting shallow particle recycling and net heterotrophy in the deep euphotic zone. These estimates open the way to fully three-dimensional global reconstructions of particle fluxes in the ocean, supported by the growing database of \emph{in situ} optical observations.