  In this article we prove that stochastic differential equation (SDE) with
Sobolev drift on compact Riemannian manifold admits a unique $\nu$-almost
everywhere stochastic invertible flow, where $\nu$ is the Riemannian measure,
which is quasi-invariant with respect to $\nu$. In particular, we extend the
well known DiPerna-Lions flows of ODEs to SDEs on Riemannian manifold.
