  We consider a nonlinear stochastic partial differential equation (SPDE) in
divergence form where the forcing term is a Gaussian noise, that is white in
time and colored in space such that the gradient of the solution is
H\"older-continuous, but not differentiable. Then, we prove a generalized
Taylor expansion of the difference between the solution to the SPDE and the
solution to its linearization around a fixed basepoint. The result is
reminiscent of the theory of (controlled) rough paths and agrees with the
general observation, that, in settings with a rough driver, subtracting the
solution to the linearized equation yields a more regular object.
