What happened to the cultural melting pot of imperial Rome?

My likely flawed assumption is that modern Italy is vastly more homogeneous than their ancient relatives. Ancient Rome, especially imperial Rome 50-200 AD, seems to have included slaves and citizens of several different cultures and origins, such as Britannia, North Africa and Syria. If we compare with Italy of the 19th or 20th century, what cultural diversity will we see and what happened to the diversity of ancient Rome?