The mosaic floor was literally taken up piece by piece from the ancient bathhouses from Ostia Antica which was the old port of Rome. The Floor dates from the third century B.C. and placed back down piece by piece in the 18th century. The mosaic floor tells the story from the battle of the Centaurs.

https://en.wikipedia.org/wiki/Baths_at_Ostia

The preservation and extensive excavations at Ostia Antica have brought to light 26 different bath complexes in the town. These range from large public baths, such as the Forum Baths, to smaller most likely private ones such as the small baths (I, XIX, 5). It is unclear from the evidence if there was a fee charged or if they were free. Baths in Ostia would have served both a hygienic and a social function like in many other parts of the Roman world. Bath construction increased after an aqueduct was built for Ostia in the early Julio-Claudian Period. Many of the baths follow simple row arrangements, with one room following the next, due to the density of buildings in Ostia. Only a few, like the Forum Baths or the Baths of the Swimmers, had the space to include palestra. Archaeologist name the bathhouses from features preserved for example the inscription of Buticoso in building I, XIV, 8 lead to the name Bath of Buticosus or the mosaic of Neptune in building II, IV, 2 lead to the Baths of Neptune. The baths in Ostia follow the standard numbering convention by archaeologists, who divided the town into five regions, numbered I to V, and then identified the individual blocks and buildings as follows: (region) I, (block) I, (building) 1.

Baths of Buticosus
This small bathhouse (I, XIV, 8) was constructed during the reign of Trajan circa 110 C.E. and remodeled in the middle of the second century C.E. This bath is typical of many of the balnea in Ostia, where the rooms are built into the established city grid leading to a chaotic interior layout often without a palaestra. In Room 4 is a black-and-white mosaic with marine animals and a man. Besides the man is an inscription EPICTETVS BVTICOSVS, giving the bath house its modern name. This man was a bathing attendant and holds a bucket and a stick. In the caldarium is another black-and-white mosaic with a marine scene of Triton and Nereid. The bath was supplied with water by a tank equipped with a noria in the adjacent Republican Sacred Area. These baths also preserved frescoes with garden images, creating an illusion of a real garden.

Baths of Neptune
East of the theater is another large square bath complex covering c. 4,400 square meters (67 meters x 67 meters) and is known as the Baths of Neptune (II, IV, 2). The structure, built late during the reign of the emperor Hadrian, was dedicated early (~139 C.E.) in the reign of Antonius Pius. At the end of the second century C.E it was restored by Gamala Iunior. The bath continued to be renovated until the 4th century C.E. The bath house is surrounded on four sides by streets and has entrances on each street. The overall design of the bathhouse was similar to those found in Pompeii, such as the Central Baths and therefore represents the next aspect of development.