And not the Soviets. It is true that many Germans fled during the war ahead of the Red Army (or were pushed out by the Red Army). But overall they comprised a relatively small percentage of final total of expelled.
In most cases it was the locals who carried all of this out. And part of the reason was that they were seething with rage over living under brutal German occupation. Another was that postwar Communist governments (backed by the Soviets, but staffed by the locals) lacked legitimacy and were eager to redistribute all of this German property to a destitute population that was not particularly keen on them. In some cases you had RW nationalists cooperating with the Communists in the expulsion process because they were both on the same page about getting rid of the Germans. And many leftover figures from interwar governments had no problem with any of this.
But Czechoslovakia, for instance, didn't even have a Communist government until 1948, when they came to power in a coup and joined the Soviet bloc. The time right after the end of the war has been dubbed the 'wild' period of expulsions, where Czechs showed very little mercy to the local German population, and made a point to get even not only through expulsions, but through mob violence as well. One of the ironies here is that wartime occupation was actually less brutal in Czechoslovkia than in Poland, but the Czechs tended to be rougher than the Poles in the expulsion process. This was not carried out at the behest of the Soviets nor with their assistance. It was a Czech thing.
Despite the Red Army's conduct at the end of the war, after it was over, in some places Germans began to see the Red Army garrison troops as more sympathetic to them than the enraged local populations.