We study diffusion of self-interstitial atoms (SIAs) in vanadium via molecular-dynamics simulations. The ⟨111⟩-split interstitials are observed to diffuse one-dimensionally at low temperature, but rotate into other ⟨111⟩ directions as the temperature is increased. The SIA diffusion is highly non-Arrhenius. At $T<600\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, this behavior arises from temperature-dependent correlations. At $T>600\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the Arrhenius expression for thermally activated diffusion breaks down when the migration barriers become small compared to the thermal energy. This leads to Arrhenius diffusion kinetics at low $T$ and diffusivity proportional to temperature at high $T$.