Coherence from vanishing second L2-Betti number

Let $X$ be an aspherical two-complex and let $G=\pi_1(X)$ be its fundamental group. Say that $G$ has trivial second $L^2$-Betti number when $b_2^{(2)}(G)=0$. Betti coherence conjecture. If $G$ has trivial second $L^2$-Betti number, then $G$ is coherent. The paper notes that a homological version follows when $G$ satisfies the strong Atiyah conjecture, but leaves the coherence conjecture open in general.