  We introduce diffusion means as location statistics on manifold data spaces.
A diffusion mean is defined as the starting point of an isotropic diffusion
with a given diffusivity. They can therefore be defined on all spaces on which
a Brownian motion can be defined and numerical calculation of sample diffusion
means is possible on a variety of spaces using the heat kernel expansion. We
present several classes of spaces, for which the heat kernel is known and
sample diffusion means can therefore be calculated. As an example, we
investigate a classic data set from directional statistics, for which the
sample Fr\'echet mean exhibits finite sample smeariness.
