  We provide a simple proof of quenched stochastic homogenization for random
environments with a mean zero, divergence-free drift under the assumption that
the drift admits a stationary $L^d$-integrable stream matrix in $d\geq 3$ or an
$L^{2+\delta}$-integrable stream matrix in $d=2$. In addition, we prove that
the environment almost surely satisfies a large-scale H\"older regularity
estimate and first-order Liouville principle.
