As already pointed out the four emperors from Venice are either to be identified as the Tetrarchs Diocletian, Maximian, Galerius and Constantius Chlorus or as the sons of Constantine the Great. The former theory is substantiated by the fact that the portraits are very similar in style and iconography to other depictions of the Tetrarchs like this one from Rome or this portrait of Galerius from Gamzigrad in Serbia.

The problem with the second theory is that although Constantine indeed had four sons, the oldest one, Crispus, had already been killed on his father's orders when the youngest, Constans, was proclaimed to be Caesar. So it doesn't really make sense to show all four of them together as emperors. A depiction of the three younger sons together with their father is equally unlikely as Constantine would probably never have shown himself as equal to his subordinate sons.

So why even propose the second theory? The thing is, we know pretty exactly were those four emperors were originaly put on display. The setting at the facade of San Marco in Venice is obviously a secondary one. Those four emperors belonged to the many trophies that the Venetians took from Constantinople after they had conquered the city in 1204 in the course of the 4th crusade. We even know were in the city they were taken from. You see, one of the four statues is missing part of his foot, his heel to be exact. Coincidentally this heel has been discovered at an archaeological dig in Istanbul and can still be seen today in the Archaeological Museum in that city. The place were it was found roughly matches the location of a public square of ancient Constantinople, the Philadelphion. The 8th century text that /u/shlin28 refered to, the Parastaseis syntomoi chronikai, tells us about a depiction of Constantine's sons that could be seen at this very place and even gave it its name. Considering this it is very likely that the four emperors from Venice are in fact the statues that the text refers to.

At the end I would like to propose a kind of harmonization of both theories. It is well known that Constantine had all kinds of ancient statuary transported to Constantinople after he refounded the city in 324/330. They were supposed to provide his new foundation with the air of history it so obviously still lacked. I think it's not all that unlikely that one of those statue groops was a depiction of the four original Tetrarchs. After all one of them, Constantius Chlorus, was his own father, another, Maximian, had been his father-in-law. Constantine would have them put up at the Philadelphion. Now we know that by the 8th century the identity of much of the statuary displayed in Constantinople had become forgotten. The Tetrarchs didn't play much of a role in the public consciousness of the city. Constantine and his sons on the other hand were still very well known. Middle Byzantine literature often attributes public monuments inside Constantinople to Constantine. I think it is very much possible that the author of the Parastaseis syntomoi chronikai simply didn't know that those portraits were originally meant to be the Tetrarchs. By then the population of Constantinople already identified them with Constantine's sons.

Eddit: There's a very interesting article about how the medieval Byzantines interpreted the ancient statuary thar surrounded them in their capital city: Cyril Mango, Antique Statuary and the Byzantine Beholder, Dumbarton Oaks Papers 17, 1963, pp. 55-75.

According to this and this, the statue could either be of the Tetrarchs or of Constantine's sons. There is a record of a statue of his sons at the Philadelphion, from where the Venice statue was taken - the relevant part from the eighth-century text is:

The so-called Philadelphion represents the sons of Constantine the Great. One of them arrived in Constantinople from Gaul after his father's death. They greeted each other with a great meeting and rejoicing, and at once erected statues of themselves in the city preserving the scene.

The most obvious flaw I can see is that the sons of Constantine never actually met in Constantinople, but that might be because the later chronicler was only repeating what he had heard from others. Constantine also only had three surviving sons by then, but perhaps one figure was supposed to represent Constantine himself? Still, some academics clearly thought that such an attribution is plausible, but I also think it is unverifiable until there is further research on this.

I've never heard of them being Constantine's sons before this honestly. There's a reason it is named after the Tetrachs. All the evidence points to it being a depiction of them. Constantine did have four sons, but considering he had one of them executed three years after his last son was born, this statue would have to date from that three year period, which makes the idea exceedingly unlikely as it depicts four adult men. Not coincidentally, all are the same, except two have beards to signify being elders.