A one-group diffusion approximation to neutral transport in a plasma is incorporated in a two-dimensional (θ-r) computational code, EPIC, coupling transport and recycling of the plasma-neutral fluids in a consistent finite discretization scheme. Boundary conditions accommodate particle recycling at the edge-core plasma interface. Neutral particle reflection from the pumping duct characterizes a given pumping system. Marginal validity of the diffusion approximation motivates extensive comparisons of the results with Monte Carlo (DEGAS) transport calculations. In prescribed and in self-consistently computed plasma solutions, the neutral diffusion results are comparable with the Monte Carlo results for radial and poloidal profiles of atomic neutral density over a wide range of limiter and divertor edge plasmas. Steady-state density and temperature contours for the Axially Symmetric Divertor Experiment (ASDEX) diverted tokamak are consistent with previous computations using fixed boundary conditions at the separatrix, but show reduced (20%) recycling attributed to the more realistic neutral atom transport by charge-exchange scattering in the diffusion model. Time-dependent plasma solutions with flux boundary conditions across the separatrix are more consistent with experimental data than results with fixed value boundary conditions at the separatrix. The flux across the separatrix is dominated by recycled particles from the edge plasma. A conclusion is that while the one-group diffusion treatment oversimplifies the physics of neutral transport, it is computationally efficient and adequate in accuracy and therefore well suited for edge plasma and for plasma-neutral recycling studies.