Sword of the Demon Hunter: Kijin Gentoushou

From Airship:
For generations, a shrine has stood in the mountain village of Kadono, and for each generation, the shrine has had an Itsukihime its shrine maiden and the maiden has had her guardian. During the Edo period, a young man named Jinta protected the town and the Itsukihime. When he confronts a strange demon in the nearby forest, it tells him that in the distant future, a Demon God will threaten all people, everywhere, and it claims that the Demon God’s rise to power springs from this very time and place, in the village of Kadono. So begins the centuries-spanning journey of a man tainted by demons, hunting through time to seek justice for what he’s lost, and to find a reason to keep on fighting.