  We propose a new method to calculate electric dipole moments induced by the
strong QCD $\theta$-term. The method is based on the gradient flow for gauge
fields and is free from renormalization ambiguities. We test our method by
computing the nucleon electric dipole moments in pure Yang-Mills theory at
several lattice spacings, enabling a first-of-its-kind continuum extrapolation.
The method is rather general and can be applied for any quantity computed in a
$\theta$ vacuum. This first application of the gradient flow has been
successful and demonstrates proof-of-principle, thereby providing a novel
method to obtain precise results for nucleon and light nuclear electric dipole
moments.
