  We consider dimension reduction for solutions of the K\"ahler-Ricci flow with
nonegative bisectional curvature. When the complex dimension $n=2$, we prove an
optimal dimension reduction theorem for complete translating K\"ahler-Ricci
solitons with nonnegative bisectional curvature. We also prove a general
dimension reduction theorem for complete ancient solutions of the
K\"ahler-Ricci flow with nonnegative bisectional curvature on noncompact
complex manifolds under a finiteness assumption on the Chern number $c^n_1$.
