Valiant's determinantal-complexity conjecture for the permanent

For a polynomial $f$, let $\mathrm{dc}(f)$ denote the least size of a matrix of affine linear forms whose determinant equals $f$. Let $\mathrm{per}_m$ denote the permanent of an $m\times m$ matrix. Valiant's conjecture. The determinantal complexity $\mathrm{dc}(\mathrm{per}_m)$ grows superpolynomially in $m$.

This would separate the permanent from determinant computations and imply the conjectured separation between algebraic branching programs and $\mathrm{VNP}$. The source gives no resolution.