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Monolayer nanoporous graphene represents an ideal membrane for molecular separations, but its practical realization is impeded by leakage through defects in the ultrathin graphene. Here, we report a multiscale leakage–sealing process that exploits the nonpolar nature and impermeability of pristine graphene to selectively block defects, resulting in a centimeter-scale membrane that can separate two fluid reservoirs by an atomically thin layer of graphene. After introducing subnanometer pores in graphene, the membrane exhibited rejection of multivalent ions and small molecules and water flux consistent with prior molecular dynamics simulations. The results indicate the feasibility of constructing defect-tolerant monolayer graphene membranes for nanofiltration, desalination, and other separation processes.