The abundance conjecture for nef divisors on varieties with trivial canonical class

Let $X$ be a projective manifold with $H^1(X,\mathcal O_X)=0$ and $K_X\sim 0$, and let $L$ be a nef divisor. Abundance conjecture for varieties with trivial canonical class. Then $L$ is semiample. The vanishing condition excludes tori; without it, the source says the expected conclusion should instead be numerical equivalence to a semiample divisor. This is presented as an expected generalisation of abundance to the $K_X$-trivial setting.