In this work we develop a variational formalism for decomposing the effect of stochastic noise on traveling waves in neural fields. The noise is decomposed into two parts: a shift of the wavefront, and a small perturbation about the wavefront. We find that the decomposition is accurate on timescales that are exponential in the inverse of the strength of the noise. The decomposition is applied to various neural field waves in product spaces, and also waves that are induced by a stimulus.