Let $X$ be a rigid Calabi-Yau variety. Does $X$ have only finitely many automorphisms?

N.B. A smooth projective variety $X$ over $\mathbb C$ is a rigid Calabi-Yau variety if $h^i(X,\mathcal O_X) =0$ for all $i>0$ and $\mathrm{H}^1(X,T_X) =0$ (or equivalently $h^{2,1}(X) = 0$).