The generation of multigroup neutron cross sections is usually the first step in the solution of reactor physics problems. This typically includes generating condensed cross section sets, collapsing the scattering kernel, and within the context of diffusion theory, computing diffusion coefficients that capture transport effects as accurately possible. Although the calculation of multigroup parameters has historically been done via deterministic methods, it is natural to think of using the Monte Carlo method due to its geometric flexibility and robust computational capabilities such as continuous energy transport. For this reason, a stochastic cross section generation method has been implemented in the Mont Carlo code MCNP5 (Brown et al, 2003) that is capable of computing macroscopic material cross sections (including angular expansions of the scattering kernel) for transport or diffusion applications. This methodology includes the capability of tallying arbitrary-order Legendre expansions of the scattering kernel. Furthermore, several approximations of the diffusion coefficient have been developed and implemented. The accuracy of these stochastic diffusion coefficients within the multigroup framework is investigated by examining a series of simple reactor problems.