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Simulations and experiments have revealed enormous transport rates through carbon nanotube (CNT) channels when a pressure gradient drives fluid flow, but comparatively little attention has been given to concentration‐driven transport despite its importance in many fields. Here, membranes are fabricated with a known number of single‐walled CNTs as fluid transport pathways to precisely quantify the diffusive flow through CNTs. Contrary to early experimental studies that assumed bulk or hindered diffusion, measurements in this work indicate that the permeability of small ions through single‐walled CNT channels is more than an order of magnitude higher than through the bulk. This flow enhancement scales with the ion free energy of transfer from bulk solutions to a nanoconfined, lower‐dielectric environment. Reported results suggest that CNT membranes can unlock dialysis processes with unprecedented …