  We define a diffeology on the Milnor classifying space of a diffeological
group $G$, constructed in a similar fashion to the topological version using an
infinite join. Besides obtaining the expected classification theorem for smooth
principal bundles, we prove the existence of a diffeological connection on any
principal bundle (with mild conditions on the bundles and groups), and apply
the theory to some examples, including some infinite-dimensional groups, as
well as irrational tori.
