Uniform diameter bound for finite-time Kähler-Ricci flow singularities

Let $\omega=\omega(t)$ be a solution of the Kähler-Ricci flow on a compact manifold $X$, defined on its maximal time interval $[0,T)$. Here ${\rm diam}(X,\omega(t))$ denotes the diameter of $X$ with respect to the metric associated to $\omega(t)$, and $C$ is a uniform constant. Diameter bound conjecture. If $T<\infty$, then

$${\rm diam}(X,\omega(t))\leq C$$

for all $t\in[0,T)$. Uniform diameter control would constrain the geometric degeneration of finite-time Kähler-Ricci flow singularities. The supplied text presents this as an expectation and gives no resolution.