Few-group diffusion equations are derived from variational principles. It is shown that by proper choice of trial function it is possible to derive a few-group theory in which interface boundary conditions of continuity of few-group fluxes and currents are obtained, even when the few-group constants are obtained by flux-adjoint weighting. The analysis is facilitated by the use of functionals that incorporate the interface condition of flux continuity by means of Lagrange multipliers. Two functionals are used to give two variants of the theory. Both functionals have as Euler equations the P-1 approximation to the time-independent, eigenvalue form of the energy-dependent transport equation. In addition, the current and flux interface boundary conditions are part of the complement of Euler conditions of the functionals. The functionals admit trial functions discontinuous in space and energy. The two functionals differ in that one has both flux and current arguments, whereas the other has only flux arguments, and yields the P-1 equations in second-order diffusion form.