The Fitzhugh-Nagumo model with diffusive coupling is known to admit a variational (energy-based) formulation, which is a result of its underlying skew-gradient structure. We show that since stationary solutions of the diffusive Fitzhugh-Nagumo model are described by self-adjoint operators, the methods of equilibrium propagation for performing credit assignment can be applied. Further, for networks with the topology of a deep residual neural network, we show that the steady state solutions also admit a Hamiltonian description, and thus the methods of Hamiltonian Echo Backpropagation can be applied. We end by deriving an explicit layer-wise Hamiltonian recurrence relation governing inference in such models.