The entire history of Europe for the past 4,000 years is of migrations from the East to the West. First the Lusitaninans, Basques, Etruscans, and Belgae, then the Celts (let's include the Gauls in that group), then the Mycenaeans, then the Greeks, then the Romans (who were Latins,), then the Franks, Angles, Saxons, and other Germanic tribes, then the Huns and Slavs. Roughly.
In the Iberian Peninsula we also had a migration from the South to the North with the Muslim conquest that started in 711, but apparently they didn't leave that big of a genetic legacy.
Yeap there does seem to be a general drift from bottom-right towards top-left on the map of europe. Except, perhaps, the vikings who went from north to south?