  Self-interacting diffusions are processes living on a compact Riemannian
manifold defined by a stochastic differential equation with a drift term
depending on the past empirical measure of the process. The asymptotics of this
measure is governed by a deterministic dynamical system and under certain
conditions it converges almost surely towards a deterministic measure (see
Bena\"im, Ledoux, Raimond (2002) and Bena\"im, Raimond (2005)). We are
interested here in the rate of this convergence. A central limit theorem is
proved. In particular, this shows that greater is the interaction repelling
faster is the convergence.
