Campana's conjecture on virtually nilpotent fundamental groups

Let $X$ be a normal complex algebraic variety. Suppose that $\pi_1(X)$ is virtually nilpotent. Campana's conjecture. Then $\pi_1(X)$ is virtually at most $2$-step nilpotent. This conjecture was formulated for compact Kähler and smooth projective varieties and asked as a question for general normal complex algebraic varieties. The paper proves it for aspherical normal varieties, while the general case remains open.