Kollár's quotient-singularity conjecture for finite covers

Let f\colon X\xymatrix@1@=15pt{\ar[r]&} Y be a finite and dominant morphism from a smooth variety $X$ onto a normal variety $Y$. Kollár's conjecture. The variety $Y$ has quotient singularities. This would explain why the bases of the fibrations considered in the paper should have at worst quotient singularities; the claim is known for dimension $2$ but remains open in higher dimension.