We just work over $\mathbb C$. Let $X \to X'$ be a resolution of singularities of a normal variety $X'$. Here $X'$ is singular and $X$ is nonsingular. We assume that $K_{X'}$ is $\mathbb Q$-Cartier so that the plurigenera of $X'$ can be defined.

I am wondering that what kind of singularities $X'$ can have such that the plurigenera of $X$ and $X'$ are equal? For example, what if $X'$ only has terminal singularities? What about any other types of singularities?