King Jumong, who founded the Korean kingdom of Goguryeo, was the son of Hae Mo-su of Buyeo who was reputed to be a "son of Heaven". Later, Goguryeo's spiritual successor state of Goryeo styled their rulers "son of heaven", but only internally. Externally, or specifically when dealing with China, the Goryeo monarchs styled themselves merely kings.
This dual system originated from a reform dating to the 1120s, and persisted till about the mid-13th century. It came to an end when Korea was reduced to the status of a vassal of China. Note that this was also the approach of the Vietnamese, whose monarchs used imperial titles domestically, but continue to deal with China as kings.
[T]he Buddhist monk Myocheong [advocated] a political reform called the chingje geonwon, or "proclaiming an emperor with a reign title." By creating the Son of Heaven out of the Goryeo monarchy, he meant to confront the Jin dynasty in the north ... [the king accepted] Myocheong's suggestions in 1129.
- Kim, Djun Kil. The History of Korea. ABC-CLIO, 2014.
In 1897, Korea was proclaimed an empire and King Gojong adopted imperial dignities. I believe that came with the "son of heaven" title, which has been tied to the imperial title since the latter's invention by Qin in Far Eastern customs, but I haven't verified this.
One of the traditional titles accorded to the rulers of ancient Tibetan was
lha sras (
lhase), literally, "son of god". This is basically equivalent to the Chinese concept of "Son of Heaven", except the Tibetan royal dynasty claimed actual divine descent.
The royal tombs have obvious Chinese prototypes, as does the sacredness of the king: he is "god son" (lha sras), corresponding to the Chinese emperor, the "Son of Heaven".
- Kitagawa, Joseph. The Religious Traditions of Asia: Religion, History, and Culture. Routledge, 2013.