Several test problems are presented for evaluating the radiation diffusion equations. For spatial transport schemes, one-dimensional problems with known analytic solutions are tested on two-dimensional domains with nonorthogonal meshes. It is shown that a scheme based on the finite element method is insensitive to grid distortions when the diffusion term is dominant. Other test problems deal with Compton scattering, specifically the one-dimensional Fokker-Planck equation coupled to an equation describing the change in electron temperature. The test problems model the evolution of a Planckian radiation field as it equilibrates with the electrons. In all cases, the numerical results are compared with the analytic ones.