Not only did art and excavation go together, so did art and literature. The Household Gods and the Temple of Aesculapius were inspired by an historical novel by Water Pater called Marius the Epicurean.
Diogenes was the leader of a philosophical school called the Cynics, which meant dog-like. Not only did Diogenes eschew the comforts and values of civil society and choose to bask in the sun and live in a tub, like any dog, he took a dim view of mankind in general. The lantern at his feet refers to his (unsuccessful) search for an honest man.
Diogenes, according to Plutarch, once asked Alexander the Great to step aside, as he was blocking Diogenes’ sunlight. Alexander was impressed by the man’s sense of his own importance, saying that “if he were not Alexander, he would choose to be Diogenes.” The women in the painting do not seem to be similarly impressed, a fact I find quite agreeable.
Waterhouse was inspired by a Wilkie Collins novel, Antonina or the Fall of Rome. Instead of defending Rome from an impending invasion by barbarians, the Emperor’s trivial pursuits and the sycophantic acquiescence of his courtiers, who bring him flowers and books instead of warning, result in the starvation and sack of his people.