We analyze the long-time self-diffusion properties of a density field theory for oil, water, and surfactant microemulsions. Specifically, we study the reduction of oil and water self-diffusion coefficients due to the complicated geometrical arrangement of oil-rich and water-rich phases in a bicontinuous microemulsion. This reduction, the tortuosity factor, is calculated by a massively-parallel, quenched Monte Carlo calculation. The direct calculation shows diffusive behavior persists to roughly 0.01 s in this system. Analytical arguments suggest that such behavior persists at longer times within the idealized quenched ensemble. The quenched ensemble becomes inappropriate at long times, due to surfactant membrane fluctuations and dynamic oil-water equilibration, and these physical effects imply that diffusive behavior continues for times longer than those directly simulated.