  We prove that diffusion equations with a space-time stationary and ergodic,
divergence-free drift homogenize in law to a deterministic stochastic partial
differential equation with Stratonovich transport noise. In the absence of
spatial ergodicity, the drift is only partially absorbed into the
skew-symmetric part of the flux through the use of an appropriately defined
stream matrix. This leaves a time-dependent, spatially-homogenous transport
which, for mildly decorrelating fields, converges to a Brownian noise with
deterministic covariance in the homogenization limit. The results apply to
uniformly elliptic, stationary and ergodic environments in which the drift
admits a suitably defined stationary and $L^2$-integrable stream matrix.
