Simplified additive divisor conjecture for shifted divisor correlations

Let $k$ and $cell$ be integers with $k,cell\ge 2$, let $\varepsilon>0$, and define

$$D_{k,cell}(x,h)=\sum_{n\le x}\tau_k(n)\tau_{cell}(n+h),$$

where $\tau_k$ is the $k$-th divisor function. Additive divisor conjecture, simplified version. Uniformly for $1\le h\le x^{1-\varepsilon}$,

$$D_{k,cell}(x,h)\sim \frac{c_{k,cell}(h)}{(k-1)!(cell-1)!}x(\log x)^{k+cell-2}$$

as $x\to\infty$, for a certain real-valued constant $c_{k,cell}(h)$. This predicts the expected leading term for additive correlations of divisor functions; the source refers to explicit descriptions of the constant elsewhere, while the general asymptotic remains conjectural.