Donaldson's convergence conjecture for the Calabi flow

Let $X$ be a compact Kähler manifold, let $\omega_0$ be an initial Kähler metric, and consider the Calabi flow in the Kähler class $[\omega_0]$. A constant scalar curvature Kähler metric (cscK metric) is a Kähler metric whose scalar curvature is constant.

Donaldson's conjecture. If the Calabi flow exists for all time and there exists a cscK metric in the Kähler class, then the Calabi flow converges to a cscK metric.

This conjecture concerns convergence of the Calabi flow under the existence of a cscK metric; the source does not state a resolution.