let $n$ denote a manifold equipped with a finite borel measure $\gamma$. a vector field $z$ on $n$ is said to be admissible with respect to $\gamma$ if $z$ admits an integration by parts formula. the measure $\gamma$ is said to be quasi-invariant under $z$ if the class of null sets of $\gamma$ is preserved by the flow generated by $z$. in this talk we study the law $\gamma$ of an elliptic diffusion process with values in a closed compact manifold. we construct a class of admissible vector fields for $\gamma$, show that $\gamma$ is quasi-invariant under these vector fields, and give a formula for the associated family of radon-nikodym derivatives $d\gamma_s\over d\gamma$.