  The kinetic Brownian motion on the cosphere bundle of a Riemannian manifold
$\mathbb{M}$ is a stochastic process that models the geodesic equation
perturbed by a random white force of size $\varepsilon$. When $\mathbb{M}$ is
compact with negative curvature we show that the $L^2$-spectrum of the
infinitesimal generator of this process converges to the Pollicott--Ruelle
resonances of $\mathbb{M}$ as $\varepsilon \rightarrow 0$.
