Fix a smooth Morse function $U\colon \mathbb{R}^{d}\to\mathbb{R}$ with finitely many critical points, and consider the solution of the stochastic differential equation \[ d\boldsymbol{x}_ε(t)=-\nabla U(\boldsymbol{x}_ε(t))\,dt \,+\,\sqrt{2ε}\, d\boldsymbol{w}_{t}\,, \] where $(\boldsymbol{w}_{t})_{t\ge0}$ represents a $d$-dimensional Brownian motion, and $ε>0$ a small parameter. Denote by $\mathcal{P}(\mathbb{R}^{d})$ the space of probability measures on $\mathbb{R}^d$, and by $\mathcal{I}_ε \colon \mathcal{P}(\mathbb{R}^{d})\to[0,\,\infty]$ the Donsker--Varadhan level two large deviations rate functional. We express $\mathcal{I}_ε$ as $\mathcal{I}_ε= ε^{-1} \mathcal{J}^{(-1)} + \mathcal{J}^{(0)} + \sum_{1\le p\le \mathfrak{q}} (1/θ^{(p)}_ε) \, \mathcal{J}^{(p)}$, where $\mathcal{J}^{(p)}\colon \mathcal{P}(\mathbb{R}^d) \to [0,+\infty]$ stand for rate functionals independent of $ε$ and $θ^{(p)}_ε$ for sequences such that $θ^{(1)}_ε\to\infty$, $θ^{(p)}_ε/ θ^{(p+1)}_ε\to 0$ for $1\le p< \mathfrak{q}$. The speeds $θ^{(p)}_ε$ correspond to the time-scales at which the diffusion $\boldsymbol{x}_ε(\cdot)$ exhibits a metastable behaviour, while the functional $\mathcal{J}^{(p)}$ represent the level two, large deviations rate functionals of the finite-state, continuous-time Markov chains which describe the evolution of the diffusion $\boldsymbol{x}_ε(\cdot)$ among the wells in the time-scale $θ^{(p)}_ε$.