The volume-growth conjecture for infinite-time Kähler-Ricci flow

Let $X$ be a compact Kähler manifold and let $\omega(t)$ be a solution of the Kähler-Ricci flow defined on $[0,\infty)$. Volume-growth conjecture. The Kodaira dimension satisfies $\kappa(X)\geqslant0$, and there is a constant $C>0$ such that

$$C^{-1}t^{\kappa(X)}\leqslant\operatorname{Vol}(X,\omega(t))\leqslant Ct^{\kappa(X)}$$

for all $t\geqslant0$. The source states that this conjecture is equivalent to the Abundance Conjecture in the general Kähler setting.