  We introduce a general framework for the study of the diffraction of waves by
cone points at high frequencies. We prove that semiclassical regularity
propagates through cone points with an almost sharp loss even when the
underlying operator has leading order terms at the conic singularity which fail
to be symmetric. We moreover show improved regularity along strictly
diffractive geodesics. Applications include high energy resolvent estimates for
complex- or matrix-valued inverse square potentials and for the Dirac-Coulomb
equation. We also prove a sharp propagation estimate for the semiclassical
conic Laplacian.
  The proofs use the semiclassical cone calculus, introduced recently by the
author, and combine radial point estimates with estimates for a scattering
problem on an exact cone. A second microlocal refinement of the calculus
captures semiclassical conormal regularity at the cone point and thus
facilitates a unified treatment of semiclassical cone and b-regularity.
