  Let $x$ denote a diffusion process defined on a closed compact manifold. In
an earlier article, the author introduced a new approach to constructing
admissible vector fields on the associated space of paths, under the assumption
of ellipticity of $x$. In this article, this method is extended to yield
similar results for degenerate diffusion processes. In particular, these
results apply to non-elliptic diffusions satisfying H\"ormander's condition.
