I've seen these discussions elsewhere for a long, long time.
On the one hand are people who claim that all migration was the result of cultural seep, with cultures slowly moving through an area and dominant cultures slowly taking over/displacing the other cultures.
On the other hand are people who claim that all migration is the result of warfare and that dominant cultures are put into place by defeating previous cultures.
The answer is almost certainly somewhere in between.
Taking examples:
We do know that the Roman legions were put under pressure by waves of incoming "barbarians" and that legions were recalled and Rome was conquered by barbarian invasions, as were large areas of the Roman Empire. I cannot really accept the idea that the Roman Empire decided to live harmoniously with Franks, Goths, Visigoths, Huns and so on and voluntarily decided to give up its territory.
When the legions left Britannia, the same pressures were present there and the island was settled by Germanic/Scandinavian people. There is archaeological evidence of settlement abandonment in the following centuries and also evidence of continuing settlement during the same time. So, some areas were abandoned and some carried on. But, a couple of centuries on, there were definitely Angle/Saxon/Jute kingdoms spread through England. The Scots invaded from Ireland, set up their kingdom in the Western Isles and also some in Wales and over the next few hundred years, spread their influence throughout Scotland, displacing the Britons and their language. Since the Picts were supposed to have been warlike, it is probable that there were battles. Similarly, there are epics of battles between the Britons and the invaders (The Men of the North in Cumbria is an example). Later on, the Danes invaded and set up the Danelaw in England and several kingdoms in Scotland and Ireland. These were definitely invasions, but there was also cultural exchanges involved.
Further east, there are examples of the Alans, Huns, Turks and Mongols who regularly moved out of the steppes and moved westwards and eastwards. Some of these were simple migrations with no conquests, but some were conquests, as attested by the Romans, for instance, who had to buy off several barbarian tribes, and the Byzantines, who finally succumbed to the Turks. Extrapolating backwards, the exact same pressures probably existed in earlier times, so the Indo-European steppe peoples probably moved eastwards and westwards in much the same fashion after around 2000BC, or perhaps earlier. Some of these would have been migrations, others may have been conquests, but if an area does not have large numbers of towns, it is difficult to describe taking over the area as a conquest. Where you have two nomadic or semi-nomadic cultures, is it a conquest when one of them forces the other one out of an area?
India is more complicated because you are talking about ethnic and religious matters as well. Broadly, Southern India does seem to have different languages to Northern India and many Northern Indian languages (including Pakistan/Bangladesh and Afghanistan) belong to the Indo-European language family. So, some kind of migration seems to have occureed, if you accept the origin of the Indo-Europeans on the steppes. Later on, the same things happened with Tamerlane, the Turkic Moghuls and the Delhi Sultanates, who introduced Islam to the area and were definitely conquerers. Alexander the Great was brought to a standstill by the various kingdoms in India, so they had military capability back then and presumably had similar capability in the past, so I would be surprised that they didn't resist wholesale movement into their areas. I don't know much about Hindu Mythology/Religion, but what i have read does seem to support the idea that at least some of the Hindu Gods were introduced by invaders and the caste system seems to have been originally Aryan.
So, it is complicated. Personally, I think that the denial of conquests is an oversimplification and that a lot of movement/migration involved warfare. Whether this warfare resulted in actual conquest or just a rebalancing of the local people depends on the particular area. But, you can't explain everything by marriages between nobles or the movement of small family groups.
