We will introduce new cosmological dynamics of the QCD axion and an axion-like particle, where the axion field circulates in the potential. Axion dark matter is produced by kinetic misalignment, which allows for a decay constant much below the prediction of the conventional evolutions. The new axion dynamics creates the baryon asymmetry of the universe through axiogenesis. For the QCD axion, the electroweak phase transition temperature is required to be higher than that in the standard model and is predicted as a function of the axion decay constant. The mechanism provides a connection between electroweak scale physics and axion physics. For an axion-like particle, assuming the standard electroweak phase transition temperature, the coupling strength of the axion to standard model particles is predicted as a function of the axion mass. The lepton number violation by Majorana neutrino masses may aid the baryogenesis scheme. In this scenario, which we call lepto-axiogenesis, we instead obtain a prediction on the mass of the Peccei-Quinn symmetry breaking field, which, in supersymmetric theories, is tied with the masses of super partners.