First off I don't really know anything about the multiverse theory, everything I post here is just my understanding from a five minute video and some reading on other parts of the interent.
When thinking of the multiverse created by quantum mechanics I don't think of it as there is an infinit amount of universes at this moment, there is however going to be an infinit amount of universes created. If you think that time started at one point, the big bang (many physicist believe space time was created during the big bang and it did not exist before then,) and propagates for an infinit amount of time then there has to be an infinite amount of universes. Because the amount of universes is a function of time, seeing as time is infinite then the amount of universes is infinite. The reason that there is not an infinite amount of universes at this moment is because there has not been an infinite amount of time that has passed, time started at the big bang and has only been around since then. Because of this there will never be a point in time which there is an infinite amount of universes, if there is never a point in time that has an infinite amount of universes then chances are there will never be two universes that are exactly the same.