Nature has protein channels (e.g., aquaporins) that preferentially transport water molecules while rejecting even the smallest hydrated ions. Aspirations to create robust synthetic counterparts have led to the development of a few one-dimensional channels. However, replicating the performance of the protein channels in these synthetic water channels remains a challenge. In addition, the dimensionality of the synthetic water channels also imposes engineering difficulties to align them in membranes. Here we show that zero-dimensional porous organic cages (POCs) with nanoscale pores can effectively reject small cations and anions while allowing fast water permeation (ca. 109 water molecules per second) on the same magnitude as that of aquaporins. Water molecules are found to preferentially flow in single-file, branched chains within the POCs. This work widens the choice of water channel morphologies for water desalination applications.