  We prove here that given a proper isometric action $K\times M\to M$ on a
complete Riemannian manifold $M$ then every continuous isometric flow on the
orbit space $M/K$ is smooth, i.e., it is the projection of an $K$-equivariant
smooth flow on the manifold $M$. As a direct corollary we infer the smoothness
of isometric actions on orbit spaces. Another relevant application of our
result concerns Molino's conjecture, which states that the partition of a
Riemannian manifold into the closures of the leaves of a singular Riemannian
foliation is still a singular Riemannian foliation. We prove Molino's
conjecture for the main class of foliations considered in his book, namely
orbit-like foliations.
