We use Liouville's theorem to map cosmic-ray anisotropy from Earth back to the local interstellar medium. After taking into the account the effects of the heliosphere, we find that the pristine anisotropy of cosmic rays in the local interstellar medium inferred from Tibet AS$\gamma$ measurements at 5 TeV is primarily a dipole due to a pitch-angle anisotropy along the interstellar magnetic field. The contributions of Compton-Getting effect, cosmic-ray density gradient and mirroring by the inhomogeneity of large-scale interstellar magnetic field are small. The dominance of dipole pitch-angle anisotropy implied that particle diffusion along magnetic flux tubes is the main mechanism of cosmic-ray transport in the local interstellar medium.