Is ulula (an owl of some kind) a diminutive? It looks like one, but I'm not familiar with a Latin word looking remotely like ula. The word appears to be onomatopoetic to some extent, but it's hard to judge whether this is the whole story. For example, ulula might be "a little thing that says 'ula'". The entry in L&S lists some cognates, and they make me suspect that the diminutive or reduplication is a Latin (and Greek?) invention. What do we know about the etymology of ulula, especially concerning diminutives? There are some related words (eg. ululare and ululamen), but they all seem to be derived from ulula.
Derivation of verbs from diminutives is not unprecedented: artus > articulus > articulare.