I honestly don't understand what the Japanese (Empress Saimei and her successor Emperor Tenji) had to gain in helping Buyeo Pung in his attempt to restore the Korean Baekje Kingdom after its fall to the joint forces of Korean Silla and Tang China in 660.
I understand the fact that the Baekje and Japanese royal houses allegedly shared a bloodline. Yet that's hardly a reason to send such a massive naval fleet. They should have known full well that Buyeo Pung's claim to the throne was tenuous and built on sand, considering how he was holed up in his last stronghold at Churyu. Empress Saimei's response to the fall of Baekje in 660 has the curiously ambiguous statement that Baekje now placed itself in protective Japanese hands with their call for aid. Did the empress have designs to acquire Baekje for herself? Or at the least establish a formidable Japanese presence on the Korean Peninsula?
On August 27th, 663 AD, the Japanese navy met the Tang Chinese navy at the Battle of Baekgong, along the Geum River of today's Jeollabuk-do province, while Silla forces fought Baekje's troops on the nearby banks of the river. The Tang fleet crushed the Japanese, who counted few survivors from this fiasco. After the battle and subsequent fall of Baekje's ally Goguryeo to both Silla and Tang in 668, many Baekje artisans and aristocrats fled to Japan. They were instrumental in building a large series of Korean-style castles in Japan for Emperor Tenji as a defensive ring against any possible attack by Silla or Tang (which shared friendly diplomatic relations with Japan shortly after, along with Buddhist missionaries). The ruins of some of these castles can still be seen today.
Did the Japanese show an interest in defending Baekje due to the desired expertise and abilities of some of its nobility? In essence, what exactly did Japan have to gain from all of this?
We certainly know what China wanted, seeing how the longtime allies Tang and Silla turned on each other due to the Tang emperor's insistence that even Silla be placed under the authority of Tang rule (i.e. The Protectorate General to Pacify the East). With the truce of 676, however, the Tang Empire was able only to hold on to territories north of the Taedong River. It was their comfort zone anyway, considering how it more or less matched the boundaries of the Lelang Commandery that the Chinese Han Dynasty had established in 108 BC with Emperor Wu's conquest of Wiman Joseon.
For those of you who have no idea where any of these kingdoms were located, here's a basic map: