We postulate the primary migration in typical source rocks is rate-limited by activated diffusion of the bitumen molecules through organic matter networks which are dominated by polymeric organic matter. The mechanism applies to both gaseous and oily hydrocarbons, determines their fluxes and retentions in source rocks, and is viable under geological and laboratory conditions. A numerical model which couples this mechanism to oil and gas generation produces bitumen concentration profiles similar to those observed in natural source beds and laboratory experiments. In pyrolysis simulations, the model reproduces the essential observations (such as the S1 and S2 peaks of Rock-Eval) and some subtle ones such as a dependence of the efflux on sample grain-size. The model emphasises the strong influence that primary migration can have on the timing and composition of hydrocarbons expelled from source rocks in nature and the laboratory.