Cold fusion reactions and excess heat production have been reported in the electrolysis of heavy water with a palladium metal cathode. Solution of the standard diffusion equation for deuterium without fusion indicates that the deuterium concentration distribution rapidly becomes constant in the palladium lattice. Solution of the nonlinear diffusion equation for deuterium undergoing fusion also gives constant deuterium concentrations, suggesting that any fusion occurs uniformly throughout the palladium lattice. The hypothesis that fusion reactions occur predominantly at the palladium surface is shown to be inconsistent with experimental data.