Local bilipschitz conjecture for quasiconformal maps of Carnot groups

Let $G$ be a Carnot group other than $\mathbb{R}^n$ or the Heisenberg group $\mathbb{H}_n$ for any $n$, and let $U,U'$ be open subsets of $G$. Let $f:U\to U'$ be a quasiconformal homeomorphism; when $U=G$, regard $f$ as a self-map of $G$. Xie's conjecture. The map $f$ is locally bilipschitz; moreover, if $U=G$, then $f$ is bilipschitz. The conjecture is motivated by the fact that, apart from Euclidean spaces and Heisenberg groups, all known examples of quasiconformal homeomorphisms in this setting are locally bilipschitz, while the source gives no resolution.