Interesting question!

The crowns you are referring to had their origin in the diadems of Hellenistic kings. This headgear, though quite simple in design (being a simple tied band, typically of white cloth; see these three images), was during the Republic strongly associated by the Romans with foreign monarchy. During Caesar's last year in life Antony presented him with a diadem during the Lupercalia, which widely disliked as an attempt by either of them to make Caesar a king (Cicero later used it to lambast Antony as slavish and dictatorial, Philippics 13.12, 13.17). Plutarch (Caesar 61) and Suetonius (Divus Julius 79) also claim that people decorated his statues with similar fillets, which he had an ambivalent reaction to.

Thus it should come as no surprise that the early emperors avoided diadems (especially as the assassination of Caesar happened shortly after the "Lupercalia incident"). Instead they tend to wear, when depicted with any headgear at all, the wreaths and "crowns" that were Roman military awards, like the laurels and oak leaves (some examples here). Posthumous (and occasionally alive) emperors could also be depicted with the radiate/solar crown, which looked more like a stereotypical spiked circlet, and which u/UndercoverClassicist has written about here.

There are some alleged examples of the contrary however. Suetonius claims that Gaius Caligula thought about assuming a diadem (Caligula 22). But this could just as easily be slander or rumours (how would Suetonius know he pondered doing something?), especially as Suetonius starts that chapter by calling Caligula a monster (the later Epitome de Caesaribus claims he actually did use a diadem). In similar fashion the late and notoriously unreliable Historia Augusta (Antoninus Heliogabalus 23) states that Elagabalus wished to wear a jewelled diadem, and did wear it privately. This could be another such malicious fiction (which the biography is absolutely full of), but the contemporary Herodian (5.3.6) does state that this ruler wore a diadem with gems before ascending as Roman emperor, as a Sun-priest in Emesa. I should also note that the laurel wreath of the Caesars was at this time often gilded and decorated with gems almost like a crown, as can be seen in this Severan family portrait. The Epitome (35.5), which, remember, stated Caligula used a diadem, also somehow claims that Aurelian was first among Romans to assume one, which is not reflected on his coins either (even though it might be argued to fit with his style of rulership).

No, to truly find emperors using diadems we have to look at the so-called Dominate period. I have often seen the introduction of the diadem ascribed to Diocletian, usually counted as the first Dominate emperor, but this is something I could not find in any ancient source. Diocletian is credited with a lot of other monarchical reforms, for instance prostration (Eutropius 9.26, Ammian 15.5.18; see also this by u/mythoplokos) and jewelled imperial dress and shoes (Eutropius, ibid), but not the introduction of diadems. The first clear evidence for it is in the reign of Constantine, who the Epitome (41.14) claims always wore one, and the Byzantine Chronicon Paschale/Alexandrinum (helpfully online in a modern translation here) states that he first appeared in a diadem with pearls and gemstones in the year 330. This is confirmed by coins that clearly show him wearing a jewelled one (examples here). This style was continued by later emperors like Julian (Ammian 21.1.4), and beyond the division of the Empire. For reading more about Byzantine crowns (something I do not know much about myself) I can recommend this comment by u/xeimevta, who also mentions the dangling pearls you referred to with the name prependoulia.

I hope you found this helpful!