Organic solvent nanofiltration (OSN) is an emerging membrane technology that could revolutionize chemical separations in numerous vital industries. Despite its significance, there remains a lack of fundamental understanding of solvent transport mechanisms in OSN membranes. Here, we use an extended Flory-Rehner theory, nonequilibrium molecular dynamic simulations, and organic solvent transport experiments to demonstrate that solvent flow in OSN membranes is driven by a pressure gradient. We show that solvent molecules migrate as clusters through interconnected pathways within the membrane pore structure, challenging the widely accepted diffusion-based view of solvent transport in OSN. We further reveal that solvent permeance is dependent on solvent affinity to the OSN membrane, which, in turn, controls the membrane pore structure. Our fundamental insights lay the scientific groundwork for the development of next-generation OSN membranes.