Were the bodies of ancient civilizations such as the Greeks and Romans accurate? If so, what kind of diet did they pursue and what types of exercises were done to achieve the physique?

I assume you are talking about the bodies of sculptures being accurate in relation to the people themselves? If so I would answer in two ways:

First, Romans enjoyed exercise just as we do. A Roman bathhouse was not simply where one went to have a bath. It is honestly more akin to a fitness club - there were hot baths, cold baths (Caldarium and Frigidarium, respectively - see where we get "scalding" and "frigid" from?), there were areas for wrestling, boxing, and swimming pools. The Baths of Caracalla are a great example of the multipurpose use of a Roman Bath complex. So, there were certainly citizens who would be more "chiseled" than others, just like today.

Most statues are obviously romanticized images of people. Particularly in the case of Emperors. Roman religion required emperor worship and the emperors wanted to present themselves as divine, especially in their physical appearance. Suetonius provides us with a fair amount of physical descriptions of emperors. For example, of Augustus, he notes that he was handsome and graceful, but very short and had bad teeth, a curled nose and unibrow. Take a look at the Augusta Prima Porta and tell me if that looks like the man Suetonius describes? Emperors often kept their official images as younger versions of themselves. Also, Suetonius tells that Claudius stammered, his knees buckled under him, he drooled often, and it's very likely that he suffered from Cerebral Palsy. However, all of his statues depict a fit, healthy and muscular young man. The only obvious deformity is his ears, which stuck out. You can always tell when you are looking at a bust or statue of Claudius when you see the ears.

So, to sum up - Romans certainly had opportunities to keep in shape and exercise. There were probably many who looked like the statues we see. However, many of the statues are highly idealized, especially when concerning an emperor.

Sources: Suetonius, Lives of the Twelve Caesars

Connolly, The Ancient City