I think that the concept that there were large population movements in the Migration period is uncontroversial. And where the 'Romans' saw barbarians at the gates, echoing a lecture I remember on the polarising discourse of barbarians and 'Romans', those 'barbarians' were not part of the Roman polity in the past.
And if they existed, were separate from the Roman polity circa the third century, and moved into that polity, what caused the tribes or peoples that crossed the Danube and the Rhine frontiers in Late Antiquity to move in the first place?
Well it actually is convtroversial to say that there were large population shifts at the time.
Many historians would argue that the "invaders" were actually relatively small warrior bands, who fought WITH the Romans as often as they fought against them, identified as part of the Empire, and were often quite well integrated into the Empire, an excellent example being the half-Vandal general Stilcho.
There has been a shift away from the idea that there was a massive movement of people from Germania to the empire at this time in part because it is so difficult to determine what would have prompted such large movements. The traditional explanations are, pressure from Nomadic Steppe peoples such as the Huns on the Germanic peoples forcing them to move to avoid war, enslavement, etc..., overpopulation of Germania, all spurred on by the weakness of the Roman state to handle such movements of people as well as large amounts of wealth there for the taking.
Some historians are now arguing that the "barbarian" invaders saw themselves as entirely congruous with the existing Roman state and modern attempts to construct a narrative about conquest and and migration are at best an oversimplification.
Each of these ideas has flaws, and I would recommend you read up further on them to get a more comprehensive view of the entire area and what was affecting the Romans and Germanic peoples, a good starting place is Peter Heather's Empire and Barbarians, or at least the first several chapters of it.
Further reading:
As mentioned above, Peter Heather's book has got quite a comprehensive overview of the traditional ideas and newer ones that historians are suggesting. His book is by no means perfect though and it does have some serious flaws.
Peter Brown's The World of Late Antiquity is another good place to start with a comprehensive view of many competing theories.