Non-vanishing conjecture for smooth varieties

Let $X$ be a smooth projective variety. Non-vanishing conjecture. If $K_X$ is pseudo-effective, then there exists an effective $\mathbb{Q}$-divisor $D$ such that

$$D\sim_{\mathbb{Q}}K_X.$$

This is the smooth-variety specialization of non-vanishing and forms part of the reduction framework relating non-vanishing, abundance, and minimal-model existence.