Ghys's alternative conjecture for diffeomorphism groups

Let $M$ be a compact manifold and let $\Gamma$ be a finitely generated group of smooth diffeomorphisms of $M$. Ghys's alternative conjecture. Either $\Gamma$ contains a free group on two generators, or $\Gamma$ preserves some measure on $M$. This is proposed as a diffeomorphism-group analogue of the Tits alternative; the source gives no resolution.