Fine-grained population maps are needed in several domains, like urban planning, environmental monitoring, public health, and humanitarian operations. Unfortunately, in many countries only aggregate census counts over large spatial units are collected, moreover, these are not always up-to-date. We present POMELO, a deep learning model that employs coarse census counts and open geodata to estimate fine-grained population maps with 100m ground sampling distance. Moreover, the model can also estimate population numbers when no census counts at all are available, by generalizing across countries. In a series of experiments for several countries in sub-Saharan Africa, the maps produced with POMELO are in good agreement with the most detailed available reference counts: disaggregation of coarse census counts reaches R2 values of 85–89%; unconstrained prediction in the absence of any counts reaches 48–69%.