Explanation: This is a marked difference in stylization that occurred during and in part because of Christianity's rise. You see some of the warning signs, however, with Diocletian, the pagan Emperor just before Constantine, the first unambiguously Christian Emperor. Diocletian had an early form of the trend because he harkened more to an eastern style of divinely-ordained despotism and a stronger emphasis on the 'right' kind of beliefs to hold (in Diocletian's case, paganism; in the later Emperors, Christianity)
There was a general trend, in the Late Roman Empire, of portraying the Emperor as more monarchial and unimpeachable, unlike the earlier, more dedicatedly nominally republican Principate/Early Empire, and the sculpture style is an outgrowth of that. As Christianity demanded orthodoxy (believing the correct thing) and not just orthopraxy (doing the correct thing), the Emperor who (effectively) decided what was and was not heresy had to be portrayed as ideal himself, at least during his reign, lest some poor souls listen to his doubters and damn themselves into unorthodox belief!
The faces become smoother and more inhuman; something more approaching the ideal and the divine. And the big, icon-like eyes. This is in stark contrast to the preferred style of the Pagan Republic and Principate eras, where the style of 'Verism' was dominant in busts, in which facial flaws were portrayed in full or even emphasized.
You can see there Julian the Apostate, at the bottom right of the Pagan Emperors, who resembles, well, the other pagans, despite the fact that Julian (who was a pagan) reigned in the middle of the era of Christianity's ascendence. This isn't completely due to religion, but because Julian was, in general, a huge throwback who idealized the Principate of the past. However, at a closer look, there is still a much smoother, more 'idealized' face; even moreso than his fellow pagan Augustus, the first Emperor of Rome, who was a propagandist par excellence and unafraid of depicting himself as near-divine.