- that Trajan fled the earthquake of 115 AD by fleeing from the Palace into the circus
- that Libanius wrote that it was on the Island, took up a quarter of the terrain and that the shorter of the four colonnaded streets on the Island ran up to it (and his various other comments on it, but no more locational than that mentioned)
- that Valens spied Aphraates scurrying past the Palace during a curfew and engaged in a conversation. This seems to situate it on the riverbank (which is corroborated by Libanius) and that there was a bridge nearby that Aphraates had crossed or was about to cross.
- Evagrius' comment that the palace had the river on its north side and "on the south there is a large portico with two stories which touch the walls of the city, and which have two high towers. Between the palace and the river is a public road leading from the city to the suburbs".
Thin pickings indeed. The information above has been employed to position the Palace at the side of the Hippodrome (in fact on the north-west side) with some sort of connection being imagined between the two structures to allow ingress and egress by the "powers that be" without them having to resort to the streets. The Palatine Palace in Rome adjoined (quite literally) the Circus Maximus and the palace of Galerius at Thessalonika was directly connected to the hippodrome. On of the best sources on the palaces of Diocletian and Galerius is "Late-Antique Palaces: The Meaning of Urban Context" by Slobodan Ćurčić in Ars Orientalis, Vol. 23, Pre-Modern Islamic Palaces (1993), pp. 67-90
Some have conjured up images of a version of Diocletian's Palace at Split, but on the Orontes banks instead of the shores of the Adriatic. Well, not a "version" almost an exact copy. This has brought with it the totally unfounded conjecture that the Palace was laid out like a military camp (in four segments) like the Palace at Split.
It is also claimed that the Palace had some sort of portico or cryptoportico facing the river, from which one could gaze to the suburbs and gardens on the other side of the river.
All these speculations may indeed be true. I take this opportunity to throw some more wood on the fire. I spent some time looking at the Split complex recently. I attach Robert Adam's reconstruction of the plan.
First I would note that while Diocletian finished the rebuilding of the Antioch complex, it had been started by Galerius so Diocletian was working with material that was already started. Split also was a retirement villa for Diocletian while the Palace in Antioch was a major administrative complex from which much of the Eastern Empire was run when the Emperors were in residence (or the "junior" Emperors and Caesar's during the Tetrarchic and Constantianian periods when split leadership prevailed). Thus all things being equal the Antioch Palace would have had vastly more functions than Split was built for and thus may have been significantly larger.
Did parts of the "older" iterations of the Palace survive these rebuildings? The Palatine Palace complex in Rome was accretive as have been more recent examples like the Louvre in Paris and the old Schloss in Berlin, so why should we imagine that Galerius leveled the old structures and rebuilt from scratch? Did the Palace include significant gardens? Libanius said it took up a quarter of the Island. Even if exaggerating that would have been a lot of territory to be exclusively covered by one structure. Did it include barracks? Was there a Praetorian Guard-like complex as is Rome?
Some (e.g. Deichmann) have imagined that the Golden Octagon might have been inside the Palace. This seems to rely almost literally upon the Split comparison(where there was an octagonal structure called the Temple of Jupiter) imagining the Octagon as a recycled Temple or a Heroon or Mausoleum.
Was the palace fortified? Did its river wall (if there was one) comprise part of the wall that Libanius describes as running around the Island "like a crown"? Did it need to be fortified? After all the Palatine was not fortified.... Split was fortified but it was in the middle of nowhere compared to Antioch.
Conclusion here.. none.. We do not know enough about the palace to claim it is a copy of Split or any other known structure. The main way to dispel this confusion involves a pick and shovel.