  We prove a uniform diameter bound for long time solutions of the normalized
Kahler-Ricci flow on an $n$-dimensional projective manifold $X$ with semi-ample
canonical bundle under the assumption that the Ricci curvature is uniformly
bounded for all time in a fixed domain containing a fibre of $X$ over its
canonical model $X_{can}$. This assumption on the Ricci curvature always holds
when the Kodaira dimension of $X$ is $n$, $n-1$ or when the general fibre of
$X$ over its canonical model is a complex torus. In particular, the normalized
Kahler-Ricci flow converges in Gromov-Hausdorff topolopy to its canonical model
when $X$ has Kodaira dimension $1$ with $K_X$ being semi-ample and the general
fibre of $X$ over its canonical model being a complex torus. We also prove the
Gromov-Hausdorff limit of collapsing Ricci-flat Kahler metrics on a
holomorphically fibred Calabi-Yau manifold is unique and is homeomorphic to the
metric completion of the corresponding twisted Kahler-Einstein metric on the
regular part of its base.
