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Animals use a small number of morphogens to pattern tissues, but it is unclear how evolution modulates morphogen signaling range to match tissues of varying sizes. Here, we used single-molecule imaging in reconstituted morphogen gradients and in tissue explants to determine that Hedgehog diffused extracellularly as a monomer, and rapidly transitioned between membrane-confined and -unconfined states. Unexpectedly, the vertebrate-specific protein SCUBE1 expanded Hedgehog gradients by accelerating the transition rates between states without affecting the relative abundance of molecules in each state. This observation could not be explained under existing models of morphogen diffusion. Instead, we developed a topology-limited diffusion model in which cell-cell gaps create diffusion barriers, which morphogens can only overcome by passing through a membrane-unconfined state. Under this model, SCUBE1 promoted Hedgehog secretion and diffusion by allowing it to transiently overcome diffusion barriers. This multiscale understanding of morphogen gradient formation unified prior models and identified knobs that nature can use to tune morphogen gradient sizes across tissues and organisms.