  Let $G$ be a reductive group and $U,U^-$ be the unipotent radicals of a pair
of opposite parabolic subgroups $P,P^-$. We prove that the DG-categories of
$U(\!(t)\!)$-equivariant and $U^-(\!(t)\!)$-equivariant D-modules on the affine
Grassmannian $Gr_G$ are canonically dual to each other. We show that the unit
object witnessing this duality is given by nearby cycles on the
Drinfeld-Gaitsgory-Vinberg interpolation Grassmannian defined in
arXiv:1805.07721. We study various properties of the mentioned nearby cycles,
in particular compare them with the nearby cycles studied in arXiv:1411.4206
and arXiv:1607.00586. We also generalize our results to the Beilinson-Drinfeld
Grassmannian $Gr_{G,X^I}$ and to the affine flag variety $Fl_G$.
