My question is, why after the Roman empire broke up did the Latin world never unify again, and ultimately Latin culture either gets replaced or fractures.
But after China gets fractured again and again their culture stays relatively united, and China as a political entity returns again and again
Was it because Rome was less Culturally homogenous?
Did the Huns and Goths directly contribute to the destruction of a united Latin world?
Did the Mulsim Conquest of Iberia and Northern Africa affect this at all?
Why didn't Tribes invade and settle China when it was politically divided at various points like the Huns and Goths?
Maybe I fundamentally misunderstand what happened in China or Rome, and my question is flawed because of this, if so can you tell me where I'm wrong?
'China' did not survive. Rather, the notion of 'China' has been continually redefined and reconstituted.
'China' as it might be understood around 1453, when the Eastern Roman Empire was finally wiped out by the Ottomans, was vastly different than 'China' was c. 200 BC, when the Roman Republic earnestly began pressing its interests in Greece at the expense of the Hellenistic kingdoms. Rome of course had its civil wars (like the Year of the Four Emperors in AD 69 (nice)) and crises (notably the Third Century Crisis), but by and large was able to reconstitute itself. While the Western Roman Empire nominally ceased to exist in AD 476, the Eastern empire remained in contiguous existence until the Fourth Crusade in 1204, having undergone major periods of resurgence, particularly under Justinian (r. 527-565), Basil II (r. 976-1025) and Alexios I (1081-1118). Let's take the contiguous Eastern Roman Empire from c.200 to 1204 as our baseline. In this time, 'China':
If we were to extend the timeline out to the fall of Constantinople in 1453, then
Got it? Don't worry if you haven't. The key thing, is that while Rome divided into East and West in 395 after the death of Theodosius I, 'China' began a much sharper division into north and south following the Jin civil wars. It became typical for north China to be ruled by dynasties originating in Inner Asia, be it the steppe (such as the Tuoba Northern Wei), Manchuria (such as the Khitan Liao or Jurchen Jin), or Tibet (notably, the Tangut Western Xia). While there were disruptions to this pattern in the form of occasional unifications under a particular state, they were largely ephemeral except under the Tang, who controlled both north and south for nearly three centuries thanks to effective employment of simultaneous strategies of legitimation: the ruling Li family was able to maintain an image of Chinese acculturation while remaining privately tied to their nomadic origins and thus retaining effectiveness in their dealings with Inner Asian constituents and powers. This division was a pattern that could theoretically have remained pretty constant: the Song lost those parts of the north that it controlled (and only ever somewhat tenuously thanks to continual Khitan incursions) after less than 150 years at the helm of a 'united China', seemingly affirming that the north would remain a hybrid zone as they would be unable to ever restore effective control over their old northern heartlands. Paradoxically, it would be the conquest of both Jin and Song by the Mongols that led to the permanent reconstitution of 'China' as a geopolitical and cultural unit that included lands both north and south of the Yangtze, and this reconstituted unit would be taken over by the Ming in 1351-68 and in turn absorbed by the Qing in 1644-62. That European geographers tended to distinguish between 'Cathay' in the north and 'China' in the south was not simply fanciful (although you can reasonably argue that it was rather inaccurate to keep doing it even in the sixteenth century), but rather reflects the reality that the north was typically politically separate from the south for most of the period from 300 to 1300.
Beyond the political shifts, there were major cultural ones as well. Buddhism was particularly favoured by the dynasties of Inner Asian origin like the Tuoba Wei or the Tang, and became rooted in the Chinese cultural landscape over the middle and latter part of the first millennium. The Song Dynasty saw the emergence of Neo-Confucianism, which would become the state ideology of the Ming. What is also noticeable is that the centres of Han Chinese culture migrated as well, out of the largely agrarian Central Plain in the north that was now broadly nomad-ruled, and towards the commericalising, urbanising south along the Yangtze and Pearl Rivers, and the Fujian and Zhejiang coasts. Commerical port cities like Hangzhou, Quanzhou and Guangzhou rose to prominence in this period, creating economic and cultural centres in regions that would have been marginal backwaters in the heyday of the Han. Today, north China remains relatively non-urbanised outside of Beijing and its metropolitan area, and a few major cities in coastal Shandong Province. If we were to talk of 'China' in AD 100, we'd be talking about a largely agrarian empire centred on the eastern portion of the region between the Yangtze and Yellow Rivers. If we were to talk of 'China' in AD 1100, we'd be talking about a commercialised, semi-maritime empire centred on the coastal regions from the Yangtze to the Pearl Deltas.
All this to say that I would disagree that 'China' 'survived' or 'returned'. 'China' as it was understood in 100 had effectively fallen by the mid-300s, and the 'China' that emerged after about 950 was a very different entity from what had come before. Or to put it another way, many 'Chinas' fell, and many different 'Chinas' replaced them.
That is a broad question, but I'll try to answer from the Roman side.
During the final days of the Western Empire, many different barbarian groups existed, but in general they all had contact with the Romans for centuries. A lot of them were employed by the Romans! The Franks were the main force guarding Gaul's frontier for a long time. The Goths even became an official unit of the military for a while. So, they didn't have some alien culture, instead they were very Romanized culturally.
After the Western Empire fell, you had a lot of successor states that came from all those groups, and they were not so different culturally from their previous situation as provinces of the Empire. They couldn't be, at the beginning - the native population was vastly superior to that of the invaders, and no one wanted to actively destroy the Roman state apparatus anyway. However, the groups were too fragmented to conquer each other, so this practical reality is a first reason for why the Latin world fractured. The Franks eventually gave rise to the Carolingians, which got closer than anyone else, but even they had their problems (by this time, it was difficult to fight the Byzantine Empire or the Caliphate). The Eastern/Byzantine Empire also tried to reunite the former Western Empire but failed - and they couldn't try again later, as they were constantly fighting the Caliphate.
After hundreds of years existing as separate entities, the various successor states eventually established their own identities that diverged over time. It's fair to question why they entered separate paths, instead of turning into small scale recreations of the Roman Empire, since their starting culture was similar.
The answer lies in the economic structure of the region: The Roman Empire was a Mediterranean trade empire. Its way of handling power, bureaucracy, the relative importance of provinces, grain supply, everything revolved around the Mediterranean trade. When you have a country that's only part of the previous Empire, you need to change your structure accordingly. You can't have the uber-rich Senatorial class of before, because the lessened trade resulted in a less rich aristocracy. You can't have the professional bureaucrats of before because you don't really need them as much in this new world. This slowly evolved to the early middle ages model, which resulted in more powerful central authority & royal courts, while relying on the approval of the people in public assemblies (case in point, the Merovingians). The Byzantines had a parallel development: After losing many regions in the Umayyad conquests they had to rethink how to organize the state, and many people like to refer to them as the Eastern Roman Empire before this reorganization and as Byzantines after that.
The main point is that this evolution occurred differently in the various regions, and by the late 6th century the former provinces didn't think of themselves as Roman anymore. Their neighbors were different from them, and they were all different from their former Roman roots.