We prove an almost sure invariance principle for diffusion driven by velocities with unbounded stationary vector potentials. The result generalizes to multiple particles motion, driven by a common velocity field and independent molecular Brownian motions.
"An Invariance Principle for Diffusion in Turbulence." Ann. Probab. 27 (2) 751 - 781, April 1999. https://doi.org/10.1214/aop/1022677385