  It is well known that the K\"ahler-Ricci flow on a K\"ahler manifold $X$
admits a long-time solution if and only if $X$ is a minimal model, i.e., the
canonical line bundle $K_X$ is nef. The abundance conjecture in algebraic
geometry predicts that $K_X$ must be semi-ample when $X$ is a projective
minimal model. We prove that if $K_X$ is semi-ample, then the diameter is
uniformly bounded for long-time solutions of the normalized K\"ahler-Ricci
flow. Our diameter estimate combined with the scalar curvature estimate in [34]
for long-time solutions of the K\"ahler-Ricci flow are natural extensions of
Perelman's diameter and scalar curvature estimates for short-time solutions on
Fano manifolds. We further prove that along the normalized K\"ahler-Ricci flow,
the Ricci curvature is uniformly bounded away from singular fibres of $X$ over
its unique algebraic canonical model $X_{can}$ if the Kodaira dimension of $X$
is one. As an application, the normalized K\"ahler-Ricci flow on a minimal
threefold $X$ always converges sequentially in Gromov-Hausdorff topology to a
compact metric space homeomorphic to its canonical model $X_{can}$, with
uniformly bounded Ricci curvature away from the critical set of the
pluricanonical map from $X$ to $X_{can}$.
