Consider a fast-slow system of ordinary differential equations of the form \[ \dot x=a(x,y)+\epsilon^{-1}b(x,y), \qquad \dot y=\epsilon^{-2}g(y), \] where it is assumed that \(b\) averages to zero under the fast flow generated by \(g\). Here \(x\in\mathbb{R}^d\) and \(y\) lies in a compact manifold. We give conditions under which solutions \(x\) to the slow equations converge to solutions \(X\) of a \(d\)-dimensional stochastic differential equation as \(\epsilon\) goes to \(0\). The limiting SDE is given explicitly.