  We investigate how to obtain various flows of K\"ahler metrics on a fixed
manifold as variations of K\"ahler reductions of a metric satisfying a given
static equation on a higher dimensional manifold. We identify static equations
that induce the geodesic equation for the Mabuchi's metric, the Calabi flow,
the pseudo-Calabi flow of Chen-Zheng and the K\"ahler-Ricci flow. In the latter
case we re-derive the V-soliton equation of La Nave-Tian.
