Peter Heather in "Empires and Barbarians" makes a good case for Rome's own success playing a major part. He explains that beyond the Rhine and Danube, the quality of the land and more primitive agricultural practices meant that areas weren't able to support large populations and often lost their ability to support even small populations after only a few generations. However, as Rome expanded to its frontiers, gradual technology transfer spread more advanced agricultural technologies deeper into Europe thanks to the porosity of Rome's borders to raiding and cross-border trade. After many generations, the result was the regions across the Rhine and Danube were able to support larger populations and more advanced societies. Meanwhile, Rome's frontiers had already been an attractive target for raids long before the peoples across the border had the ability to support larger polities. As Rome weakened, larger, more advanced barbarian polities had the kind of organization and power for more substantial raiding. Given their semi-nomadic past, they also had less aversion to migration, and thus were more able to move as large migrating groups.

There as also the Huns, which usually fall into the narrative that they came raiding across the Pontic Steppe, displacing tribes as they came and forcing them towards Rome out of desperation. However, the beginning stages of the Migration Period seem to predate the Huns and fall more in line with Heather's idea of technology transfer - the Marcomannic Wars took place in the latter half of the Second Century and were on a scale far larger than any Germanic raids Rome had suffered thus far, and in the Third Century Gothic raiders were raiding all over the Black Sea and Balkans, and even making it as far as Cyprus. The Huns may have displaced people, but they didn't create a refugee crisis as it's often portrayed.

As for the style of migration, it varied widely. They could consist of very small units moving over the span of generations or be more substantial single units like Alaric's Visigoths in the early 5th Century. The big thing to remember is that the migrations were rarely as "clean" as they're portrayed. Long-term piecemeal migrations like that of the Goths from the Baltic to the Pontic Steppe weren't complete population transplants, nor did they completely displace the populations where they arrived. Some of the "old" people remained at both the start and end points of migration, and often cultural elements would combine as the new migrants moved in. Larger single migrations, on the other hand, tended to consist of more diverse groups than they're labeled - Alaric's Visigoths, for example, had people from most of the major groups that had settled in the Balkans.