It is well known that Kronheimer classified all hyperk?hler ALE $4$-manifolds. In particular, any such manifold must be diffeomorphic to the minimal resolution of $\mathbb C^2/\Gamma$ for a finite group $\Gamma \subset SU(2)$.

Given a manifold $M$ which is diffeomorphic to the minimal resolution of $\mathbb C^2/\Gamma$, is the ALE metric unique on $M$, up to isometry and rescaling?