  We prove central limit theorem under diffusive scaling for the displacement
of a random walk on ${\mathbb Z}^d$ in stationary divergence-free random drift
field, under the ${\mathcal H}_{-1}$-condition imposed on the drift field. The
condition is equivalent to assuming that the stream tensor be stationary and
square integrable. This improves the best existing result of Komorowski, Landim
and Olla (2012), where it is assumed that the stream tensor be in ${\mathcal
L}^{\max\{2+\delta,d\}}$, with $\delta>0$. Our proof relies on the relaxed
sector condition of Horv\'ath, T\'oth and Vet\H{o} (2012), and is technically
rather simpler than existing earlier proofs of similar results by Oelschl\"ager
(1988) and Komorowski, Landim, Olla (2012).
