  We apply the gradient flow on a color-electric two-point function that
encodes the heavy quark momentum diffusion coefficient. The simulations are
done on fine isotropic lattices in the quenched approximation at $1.5\,T_c$.
The continuum extrapolation is performed at fixed flow time followed by a
second extrapolation to zero flow time. Perturbative calculations of this
correlation function under Wilson flow are used to enhance the extrapolations
of the non-perturbative lattice correlator. The final estimate for the
continuum correlator at zero flow time largely agrees with one obtained from a
previous study using the multi-level algorithm. We perform a spectral
reconstruction based on perturbative model fits to estimate the heavy quark
momentum diffusion coefficient. The approach we present here yields
high-precision data for the correlator and is also applicable for actions with
dynamical fermions.
