Recently, a considerable amount of work has been done to construct diffusion processes on non (necessarily) locally compact state spaces \(E\) associated with symmetric Dirichlet forms on \(L^ 2(E;\mu)\). One essential assumption which was used for these constructions (and which has been proved to hold in many applications) is that the (1-)capacity associated with the given Dirichlet form is tight. The purpose of this note is to prove the converse, i.e., the (1-)capacity is tight if the Dirichlet form has an associated diffusion. Meanwhile, this result and its proof have been used as an essential ingredient for the proof of the analytic characterization of all not necessarily symmetric Dirichlet forms having an associated right continuous strong Markov process [cf. Z. M. Ma and M. Röckner, Introduction to the theory of (non-symmetric) Dirichlet forms (Springer, 1992)].