See, offhanded that it may have been, and invasion of Persia is a really interesting idea. I'm not sure it would happen, and this is why.
Attila invading created a huge pressure from those fleeing before him, against the WRE and ERE. If he then turns around and takes his forces to Persia, he adds another Empire that has interests in destroying him, and gives the WRE a breather.
I wonder if the WRE and ERE could use the time given by a Hunnic invasion of Persia (via the Caucauses or Central Asia) to turn the foederati on Germania - paying them in land grants, or offering protection to the now resettled peoples. This moves the battlefield out of Roman territory, and that frontier can be prepared for the Huns.
It'd be an interesting turn of events, turning the Pax Romana on its head - the Romans (probably Western Rome) will be expect to protect the Germans, in exchange for some tribute, for fear of outside forces.
As I said before, I don't think it is the wisest idea, half of the reason the Huns were so strong was that they forced other tribes to serve/work with them, which snowballed, taking these people to Persia, or reducing the pressure, allows someone else to step in. But then again, Persia is pretty rich at this point - and an abrupt Sassanid Empire would drastically change history. Especially if his ideas of a Scythian Empire involve a Persian client state. I can't imagine it surviving his death, but - anything to give the WRE a breather and the ERE a leg up in the future.
This might be the most roundabout butterflying of Islam that isn't just "PoD before time period in question", but fundamentally changes the geopolitics of the region so that Islam, butterflies permitted, might be unable to defeat the ERE that hasn't had to fight a full-strength Persia (or is even destroyed as they've exhausted themselves fighting the Huns).