fluid dynamics - How does a converging-diverging nozzle not violate conservation of energy?

Disclaimer: I know absolutely nothing about fluid dynamics, and very little about physics in general. THis may be a really dumb question.

Now, at subsonic speeds, converging and diverging nozzles behave intuitively. When you have air moving through a converging nozzle, the area goes down, so naturally it has to speed up to maintain conservation of momentum (assuming it doesn't compress or heat up). When air moves through a diverging nozzle, the opposite happens.

Now apparently, supersonic air does the opposite: it slows down when converging and speeds up when diverging. Okay?

Apparently there's a type of nozzle that is often used in rocket and jet engines, called a converging-diverging nozzle, that accelerates air by first converging so the air speeds up to the speed of sound, then diverging, accelerating it to supersonic speeds.

Now wait a minute. So subsonic air enters, and magically supersonic air, at the same cross-section area, exits? How could this possibly work? It seems like a converging-diverging nozzle with the same entry and exit diameter can be used as a perpetual-motion ramjet. Obviously, this isn't the case. What am I missing?