  A singular foliation $\mathcal F$ gives a partition of a manifold $M$ into
leaves whose dimension may vary. Associated to a singular foliation are two
complexes, that of the diffeological differential forms on the leaf space $M /
\mathcal F$, and that of the basic differential forms on $M$. We prove the
pullback by the quotient map provides an isomorphism of these complexes in the
following cases: when $\mathcal F$ is a regular foliation, when points in the
leaves of the same dimension assemble into an embedded (more generally,
diffeological) submanifold of $M$, and, as a special case of the latter, when
$\mathcal F$ is induced by a linearizable Lie groupoid.
