Reflected diffusions arise in many contexts. We identify a rather general condition under which these diffusions belong to the class of so-called Dirichlet processes, which are a generalization of continuous semimartingales that admit many nice properties, including an Ito formula. We also provide an example arising from applications, in which the reflected diffusion fails to be a semimartingale, but belongs to the class of Dirichlet processes. This is partly based on joint work with Weining Kang.