  We investigate the in-medium modifications of heavy quarkonia in the vector
channel and the heavy quark diffusion coefficient by comparing Euclidean
correlators from the lattice to a perturbative spectral function. On the
lattice side, we work with continuum extrapolated data from four different
large and fine lattices with Clover-improved Wilson fermions in the quenched
approximation at five temperatures (0.75, 1.1, 1.3, 1.5 and 2.25$T_c$). On the
perturbative side, we use a combination of pNRQCD and vacuum asymptotics to
describe the spectral function. After accounting for systematic errors, we
obtain a spectral function that is suited to describe the bound state region.
This spectral function describes charmonium well without a resonance peak at
any of our analyzed temperatures above $T_c$, while we observe a thermally
broadened resonance peak for bottomonium that is only melted at our largest
temperature, $2.25T_c$. For the transport contribution we assume a Breit-Wigner
shaped peak and find that the drag coefficient of charm quarks is larger than
that of bottom quarks.
