AbstractA diffusion theory for the asymptotic transport scalar flux is derived from the monoenergetic transport equation in slab geometry. By allowing the scalar flux to be discontinuous at a material property and/or an external-source discontinuity, the theory is able to predict exact asymptotic transport-theory behavior for two standard halfspace problems. A supplementary diffusion-like theory is developed to treat the non-asymptotic flux. The total (asymptotic plus non-asymptotic) formalism yields a continuous scalar flux distribution and gives exact transport -theory leakage from a halfspace with a spatially-constant source. Numerous numerical comparisons indicate that the theory proposed here is significantly more accurate than classical (P1) diffusion theory. The complexity of both the asymptotic and non-asymptotic formalisms is comparable with that of theP1method. Finally, the entire formalism is generalized to three dimensions in rectilinear- and curvilinear-coordinate systems.