Thomassen's conjecture on balanced clique subdivisions

Let $G$ be a graph, let $d(G)$ denote its average degree, and let a balanced $K_t$-subdivision be a subdivision of $K_t$ in which all subdivided edge-paths have the same length. Thomassen's conjecture. For any constant $t\in\mathbb{N}$, there exists a function $g(t)$ such that every graph $G$ with $d(G)\geq g(t)$ contains a balanced $K_t$-subdivision. This is posed as a strengthening related to Mader's conjecture; the supplied text does not state whether it has been resolved.