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We develop a potential theoretic approach to the problem of metastability for reversible diffusion processes with generators of the form $-ϵ\Delta +\nabla F(·)\nabla$ on ${ℝ}^d$ or subsets of ${ℝ}^d$, where $F$ is a smooth function with finitely many local minima. In analogy to previous work on discrete Markov chains, we show that metastable exit times from the attractive domains of the minima of $F$ can be related, up to multiplicative errors that tend to one as $ϵ\downarrow 0$, to the capacities of suitably constructed sets. We show that these capacities...