  We present models in which axions have large couplings to hadrons while
remaining naturally light. By assigning $U(1)_{PQ}$ charges to Standard Model
quarks such that $U(1)_{PQ}$ is not anomalous under QCD, the derivative
couplings naturally arise while no potential is generated for the axion upon
QCD confinement. We present simple models that implement this idea both for an
axion-like particle and for the QCD axion. We show that both models lead to
sizable flavor violations that could be probed by future experiments. Our
construction shows that the axion coupling to hadrons can be essentially
independent from its mass and thus motivates experimental searches in a wide
range of axion parameter space.
