  Let $X$ be a complex $K3$ surface, $Diff(X)$ the group of diffeomorphisms of
$X$ and $Diff(X)_0$ the identity component. We prove that the fundamental group
of $Diff(X)_0$ contains a free abelian group of countably infinite rank as a
direct summand. The summand is detected using families Seiberg--Witten
invariants. The moduli space of Einstein metrics on $X$ is used as a key
ingredient in the proof.
