  In the preceding paper, we have constructed a compactly generated model
structure on the category $\dcal$ of diffeological spaces together with the
adjoint pairs $|\ |_\dcal : \scal \rightleftarrows \dcal : S^\dcal$ and
$\tilde{\cdot} : \dcal \rightleftarrows \ccal^0 : R$, where $\scal$ and
$\ccal^0$ denote the category of simplicial sets and that of arc-generated
spaces, respectively. In this paper, we show that $(|\ |_\dcal, S^\dcal)$ and
$(\tilde{\cdot}, R)$ are pairs of Quillen equivalences. Since our approach
developed in the preceding paper applies to the category $\ccal h$ of Chen
spaces as well, $\ccal h$ is also a compactly generated model category. We also
show that the adjoint pair $\mathfrak{S}_\mathfrak{o} : \ccal h
\rightleftarrows \dcal : \mathfrak{Ch}^\sharp$ introduced by Stacey is a pair
of Quillen equivalences.
