So I've just come back from visiting the Uffizi in Florence, and one of the first things that's pretty incredible to see is medieval painting from the early 1300's, where the painters displayed a poor understanding of perspective and the anatomy of the human body, side-by-side with painting from the late sixteenth and early seventeenth centuries, where the understanding of mathematical perspective is complete and human bodies and faces look entirely lifelike. Now, the Romans weren't nearly quite so badly off as the medieval painters—if you take a look at some of the examples of their fresco painting from Pompeii, you can see that their understanding of how bodies worked was not nearly as bad as it got during the bad old days of the early fourteenth century—but there were still some things that the Romans didn't ever have: the two most important were probably oil painting and perspective.
Let's say some bright young Roman painter tries
the experiment done OTL by Filippo Brunelleschi, and develops true one-point mathematical perspective to use in his paintings. This could be whenever, but let's put his discovery right around the time of the founding of the Empire, to give it room to grow and develop before any kind of collapse.
It seems self-evident that an advance in understanding like this would cause it to spread among fellow painters, but would it? Let's say it does—is it enough to avert the erosion in skill that we see OTL from the fall of the Roman Empire to the Renaissance? Does it lead to an increase in production or prestige of painting earlier, and what kinds of knock-on effects might result from that? Could it even do enough to change history?
If this wouldn't be enough (or enough on its own), how about oil painting (which we have evidence existing in Afghanistan in the 7th century, but which didn't gain popularity in Europe until the 1400s)? Would these upgrades, in ability and possibly in prestige, lead to a community of artists like the Italians and the Dutch during the Renaissance?
The image I get from these oil-painting Romans armed with mathematical perspective is a bunch of first-century Botticellis, Raphaels, and Titians painting the types of scenes from classical mythology that were quite popular during the Renaissance. The difference in this case would be that they would be painted during the time when the worship of such gods was commonplace throughout the Empire. This kind of artistic innovation, if it has great enough effects on society, might even allow for the survival of the Roman pantheon in some form.