Migration had and has always been a common feature of European life in the Iron Age and up to the Medieval period. The Roman Empire, however, created a 'line' or frontier running straight through Europe, introducing the concept of 'crossing' the border and extensively regulating passage, which previously (and subsequently) would be free. This also included the creation of 'others' in the peoples who lived beyond the frontier. So while before (and outside) of the Roman Empire, migration would have been much more fluid and dynamic, directly after all the ethnic units that the Romans had caused to form suddenly had the possibility to cross a frontier, where previously none had existed. This only slowed down again (as a process) when the barbarian peoples had settled, and the distinction between formerly-Roman and barbarian had become less significant. While migration on a smaller scale certainly would have continued, it was no longer necessary to cross the border in larger groups and take your ethnic identity with you. It was now, as it was before, more possible to simply blend in to existing local power structures.

Note also that there was probably much more movement of people (migration) during the Empire than there was in the period after it, as the wealth gradient (and the possibility for secure jobs, or social mobility) across Europe would have been much stronger. However, during the Empire migrants were usually simply taken up in already multi-ethnic communities, where original ethnicity was simply less relevant.