Repost from the other thread:

It's a moralist's answer to the question 'Why Rome fell?' Because it became decadent, of course. The argument is that as soon as loose sexual morals enter the society, it led to their downfall. While glossing over the fact that hundreds of years of killing, burning, raping and pillaging that their armies got off to isn't what we would call moral, and that the last really debauched emperor was probably Elagabalus, 200+ years before what we call the fall of the Western Roman Empire.

The idea is disputed by pretty much every historian but it's strong in the popular imagination. The whole point of the tale isn't to be factually correct anyway, it's to provide a basis for transplanting the idea of 'loose sexual morals lead to downfall of society' into the historical context to give it justification.

You can see it in a lot of depictions of ancient Rome, from the movie Satyricon, the book on my shelf titled 'Sex life of the Roman Emperors' (which is what happens when you tell your mates you're interested in Roman history) to HBO's series Rome.

Now on the question of Roman virtue:

There was certainly an expectation of public morality in polite society. Roman writers often lamented the loss of morals in society, Hellenization corrupting the good Roman people, and so on.

The concept of dignitas was a very powerful one. It's most easily explained as a combination of dignity, public reputation, and a person's good name, and they took it very seriously. There certainly would be strong societal control of sexual norms, especially of women ("Caesar's wife must be beyond suspicion"), as is usually the case in patriarchal societies. Atia Balba Caesonia, mother of Augustus, was seen as one of the examples of virtuous Roman matrons, and Tacitus says this of her: "In her presence no baseness could be prosecuted or poorly-educated attitude made without it considered a serious offense. Governed by religion and your life with the utmost delicacy involved not only in their affairs as their juvenile entertainment and games."
Men sleeping around with other women certainly wasn't condemned in society(EDIT: correction, as long as it wasn't married women or unmarried daughters), and Caesar, for instance, used this to make cuckolds out of his political opponents (EDIT: well, more precisely, he did it publicly despite the fact that it broke social norms, much like his public bribery).

However, public morals is one thing, and what went on behind closed doors another. It's hard to believe that all of them were as upright behind closed doors.

From what we know of Roman people in general: that they enjoyed gladiator fights, chariot races and rather vulgar form of theater (in which women weren't allowed for a long time because it was thought to be inappropriate), and the abundance of vulgar graffiti, that it's hard to believe that the aristocracy was so refined and so different from regular people anywhere except in their minds.

We certainly know the example of Sulla, who when he retired brought his long-time male lover with him and made no secret of it. He certainly did make secret of it before he became dictator, because something like that would have killed his chances of ever climbing the political ladder by the moral standards of the day. So the expectations of public morals were a very present force, but there was certainly room for getting away with a lot as long as you kept up pretenses. The existence of slaves in society must have made it even easier to get away with a lot on victims that had nowhere to run.

Some of the graffiti from Pompeii, by the way, is just fascinatingly vulgar:

"(Bar/Brothel of Innulus and Papilio) Weep, you girls. My penis has given you up. Now it penetrates men’s behinds. Goodbye, wondrous femininity!"

(peristyle of the Tavern of Verecundus) Restitutus says: “Restituta, take off your tunic, please, and show us your hairy privates”.

(Bar of Athictus; right of the door) I screwed the barmaid

(on the wall in the street) "Theophilus, don’t perform oral sex on girls against the city wall like a dog"

So in conclusion, yes, their society was what we would consider quite vulgar and brutal, but no, this has nothing to do with the collapse of their society, because it was like that at the time of their greatest power.

EDIT: edited to make it more coherent

EDIT2: fixed some errors

Also repost (and elaboration) of my post from the other thread. Specifically regarding the alleged sadism and perceived moral degeneracy and corruption of some Roman emperors - for example Caligula whom you mentioned - which probably also contributes a fair bit to this notion of Roman debauchery.

Now it's not entirely sure to what extent these emperors really were so corrupt, but I do know for example that Diocletian, who was a fairly successful emperor (especially compared to his predecessors from the mid 3rd century) was strongly vilified and his negative traits exaggerated (especially in contrast with emperor Constantine who made Christianity the state religion) by Christian writers later on because he was the last emperor to really persecute Christians.
[src: How Rome Fell: Death of a Superpower by Adrian Goldsworthy]

Then there are also historians like Tacitus who somewhat glorified the idea of a 'noble savage' in the areas beyond the frontiers of the Roman Empire in his book Germania (and I think also Agricola) as a means of providing contrast with what he considered to be the moral corruption of Roman society.

Earlier writers could similarly very well have had political motivations (which are a no-go if you want something resembling objective historiography) of some sort or another when writing about the decadence and corruption of Roman society and emperors like Caligula for example but I can't vouch for this - it might as well be that these reports are true to a considerable degree.