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According to Siege Warfare and Military Organization in the Successor States (400-800 AD) (pages 365-6), the formidable poliorcetic abilities of the Huns under Attila came not only from the Romans, but also from a prior exposure in the Near, Middle and Far East to other civilizations skilled in siege warfare:
They may therefore have been familiar with poliorcetics and advanced technology from China and central Eurasia over several centuries. By all accounts, in the age of Attila they had certainly been in contact with the Persians and Central Asian polities skilled in siege warfare for over a century.
This would infer that they not only used captured and deserted Roman engineers to build their siege engines, but had their own native siege engineers. As the skill necessary to make their fine composite bows was arguably even greater than that necessary to make a siege tower, this is by no means impossible to imagine.
Although it makes only a passing reference to their ability in siege warfare, The World of The Huns: Studies in Their History and Culture contains an entire chapter on their Warfare, including some circumstantial evidence that they may have had stirrups made from perishable materials.
Upvote:3
Any answer is going to be speculative, but a 'learning siege warfare by contact' explanation begs the question of why Germans and Goths, living on the edge of Rome for centuries did not do the same thing.
A difference between the Goths and the Hunnic Empire that might explain the result is that Gothic tribes were ethnic units while the Huns added whole peoples (including Goths) to their empire en-masse and gave individuals a real ability to integrate into the decision making ranks of the Huns. There is a description from an envoy to the Huns of meeting a ex-Roman who was now a mid-range chief.
The difference might be the richer rewards for those who could do that job available as an energetic siege-man in the Huns.