  Breaking the symmetry in a coupled wave system can result in unusual
amplification behavior. In the case of difference parametric amplification the
resonant pump frequency is equal to the difference, instead of the sum,
frequency of the normal modes. We show that sign reversal in the symmetry
relation of parametric coupling give rise to difference parametric
amplification as a dual of optical parametric amplification. For optical
systems, our result can potentially be used for efficient XUV amplification.
