Polynomial Diameter Conjecture for polytope graphs

For a polytope or polyhedron $P$ of dimension $d$ with $n$ facets, let $G(P)$ denote its graph.

Polynomial Diameter Conjecture. Is there a polynomial function $f(n,d)$ such that

$$\operatorname{diam}(G(P)) \leq f(n,d)?$$

The source states that no polynomial upper bound was known for polytope diameters. The conjecture remains open in the supplied material.