Both Orpheus and Izanagi lose their wives to the underworlds, travel to the said underworlds to retrieve them, and are told that their wives can come back up with them if they promise to not look at them until they've reached the surface. Both men inevitably break this promise and return to the living world alone. Is there some connection between Greece and Japan that made these stories so similar, or is it just a coincidence?
The great North American folklorist Stith Thompson (1885-1976) discusses this motif in The Folktale (1946). Parallels for this story are international, and a great deal of scholarship addressed the Orpheus parallels among American Indians.
Folklorists seeks to understand genetic relationships between similar stories, and lacking a link, they then consider the universal factors of humanity that cause parallel development. The general conclusion is that the occurrences of the motif in pre-contact North American oral tradition is coincidental. The Orpheus story obviously had an enormous influence on subsequent European culture, manifesting in subsequent pieces of literature after the Greek myth was recorded. I cannot find a reference to the motif in Asia, nor can I find whether it is genetically linked to Orpheus. But it need not be linked as indicated by the Native American parallel. My inclination would be to say that they are separate phenomena with the human condition as the common denominator.