What needs to happen so that the Roman Empire is divided into several smaller Empires and no one manages to reunite the empire? So similar to the Diadochi.
Well, the Romano-Germans kingdoms are basically this : they were all based on Late Imperial institutions, the rupture really happening in the late VIIIth/IXth centuries.
EDIT : Ninja'ed by TheYoungPretender
That said, I think that's not what you're expecting as an answer so, there's an old idea of mine.
With an harsher IIIrd century crisis, with a more widespread "provincialism".
You could just pick among early Aurelian's reign usurpers. You don't even need that the "official" emperor fails in battle : Gallienus was skilled, and it didn't prevented several rebellions or secessions.
Eventually, you'd end with a more or less stable situation, with more or less autonomous if not independent regions (altough less ruled by usurpers, that having leaders de facto aknowledging Roman rule, but acting on their own. That said, you could have some usurpers, as Gaul's, formally acknowledging some sort of "suzerainty").
Something we could call a "ducal" system (reference to the Dux Oriens title that Palmyrenians had, more or less vice-emperor or co-emperor) with Dux Hispaniae, Dux Occidens, etc. on a military-based command.
While organised, the Barbarian peoples weren't as strong they became later trough a process of structuration (with Roman support, concious or not).
You may have a more gradual Barbarian presence, as auxiliaries/laeti/foederati, than a general takeover at least in a first time.
Maybe ending as Barbarians eventually turning into patricians, à la Odoacer, ruling de facto over a given region in the name of the duke and/or emperor.
Eventually, the roman Duchies could form post-Imperial roman states that you're looking for.