In 1274, Kublai Khan launched his first invasion of Japan. Which ended quite well...for the Japanese. Because the Mongols had lost a few hundred ships and tens of thousands of men to typhoons which sank their hastily-made ships and riverboats that they decided to take to sea because Kublai really wanted Japan conquered. Then he tried again. And it went even better...for the Japanese. Because the Japanese were more prepared this time and the Mongols lost even more ships and men to the storms. And maybe they had a third invasion planned but Kublai died and then the Yuan didn't ever bother with the Japanese again because of how much was lost for absolutely nothing but humiliation.
Now, the Mongols weren't exactly a naval people and Kublai wanted Japan under his heel as quickly as possible but that doesn't mean they had to invade in 1274. After all, China had not been fully conquered and the Vietnamese are refusing to be fully subservient to the Yuan.
What if, instead of rushing to invade Japan and spending a year on a fleet that ought to have taken five years minimum to build, Kublai Khan decided to take his time and build a proper fleet before trying his luck with the Japanese? Along with any territorial changes (noting here how unlikely a full conquest was), how would that change up the diplomatic and cultural scene in East Asia?
Or, alternatively, he just decides against it (say the Goryeo king doesn't offer the same level of encouragement/naval support or conquering the Song takes a bit longer. Or the Vietnamese spit at him earlier and that keeps him occupied until death) and dedicates the resources to expansion elsewhere, thereby removing the costs of preparing hundreds/thousands of ships and tens of thousands of men for Japan and losing them all. What then? Would the Yuan stay afloat longer? Does Japan still develop the unconquerable mindset they retained until WWII?