  We study regularizations of Schwartz distributions on a complete Riemannian
manifold $M$. These approximations are based on families of smoothing operators
obtained from the solution operator to the wave equation on $M$ derived from
the metric Laplacian. The resulting global regularization processes are optimal
in the sense that they preserve the microlocal structure of distributions,
commute with isometries and provide sheaf embeddings into algebras of
generalized functions on $M$.
