We prove that the solution of a system of random ordinary
differential equations $d\mathbf{X}(t)/dt = \mathbf{V}(t, \mathbf{X}(t))$ with
diffusive scaling, $\mathbf{X}_{\varepsilon}(t) = \varepsilon \mathbf{X}(t/
\varepsilon^2)$, converges weakly to a Brownian motion when $\varepsilon
\downarrow 0$. We assume that $\mathbf{V}(t, \mathbf{x}), t \epsilon R,
\mathbf{x} \epsilon R^d$ is a d-dimensional, random, incompressible,
stationary Gaussian field which has mean zero and decorrelates in finite
time.