This work develops a global estimate of vertically resolved cloud droplet number concentration (<em>N<sub>d</sub></em>) by combining reanalysis data, satellite retrievals, ground-based observations, and field campaign measurements. This is accomplished by developing a neural-network estimator, termed NDnet, that uses satellite-retrieved cloud properties to infer three-dimensional <em>N<sub>d</sub></em> fields. Training proceeds in two stages, with a prior network first emulating a reanalysis and then being refined using observations to impose a global observational constraint. Probabilistic objective functions account for observational and representativeness errors and provide an explicit estimate of uncertainty in <em>N<sub>d</sub></em>. Applied over the satellite record, NDnet produces a more gradual decrease of <em>N<sub>d</sub></em> with altitude than suggested by the reanalysis data and higher <em>N<sub>d</sub></em> at high latitudes. The resulting fields also show substantial vertical heterogeneity, particularly in tropical and subtropical regions and at high altitude. The three-dimensional <em>N<sub>d</sub></em> dataset can be compared directly with model output and provides a new constraint for evaluating aerosol–cloud interactions in atmospheric models.