  The axion mass receives a large correction from small instantons if the QCD
gets strongly coupled at high energies. We discuss the size of the new CP
violating phases caused by the fact that the small instantons are sensitive to
the UV physics. We also discuss the effects of the mass correction on the axion
abundance of the Universe. Taking the small-instanton contributions into
account, we propose a natural scenario of axion dark matter where the axion
decay constant is as large as $10^{15\text{-}16}$GeV. The scenario works in the
high-scale inflation models.
