In this work, we derive and test variational discontinuity factors (DFs) for the asymptotic homogenized diffusion equation. We begin with a functional for optimally estimating the reactor multiplication factor, then introduce asymptotic expressions for the forward and adjoint angular fluxes, and finally require that all first-order error terms vanish. In this way, the reactor multiplication factor can be calculated with second-order error. The analysis leads to (1) an alternate derivation of the asymptotic homogenized diffusion equation, (2) variational boundary conditions for large periodic systems, and (3) variational DFs to be applied between adjacent periodic regions (e.g., fuel assemblies). Numerical tests show that applying the variational DFs to the asymptotic homogenized diffusion equation yields the most accurate estimates of the reactor multiplication factor compared to other DFs for a wide range of problems. However, the resulting assembly powers are less accurate than those obtained using other DFs for many realistic problems.