While the notion of a balance is not strictly correct in the context of a wallet, it is something that has presented some confusion for me in the context of an HD wallet, especially when importing a seed into a new wallet.

It is to my understanding that with an HD wallet you can generate a tree structure of infinite depth, but with such a structure, how would a wallet feasibly verify the unspent transaction outputs (UTXOs) if it would have to check the entire blockchain for the addresses that the wallet can generate?