Modern submarine ascents usually involve specialized suits, but they were previously done without them. They are actually what most dive agencies would call a buoyant ascent rather than a CESA, but the difference is minor. The difference between a CESA and a buoyant ascent is primarily speed. In a CESA, the diver ascends at a controlled rate of speed (that's the C in CESA), not much more than would be done normally. In a buoyant ascent, the diver inflates and/or drops weights in order to make a more rapid ascent. Buoyant ascents are recommended for deeper depths. You can turn a CESA into a buoyant ascent at any point in the ascent.
Here is a modern video showing two ascents in a naval training tower. The second uses a specialized suit. The first uses a simple flotation device. Note the amount of air being released through the mouth.
This a more vintage video (1958) from the days when this method of submarine escape was first used by the US Navy. I like this video better because the trainees are using almost no gear, and the video shows every step, starting with the initial HUGE exhalation.
The things to notice are how much air is expelled before the ascent begins, and how much air is still available for exhalation after that.
This contrasts mightily with horizontal CESA training, in which there is little to no air expansion, and the ability of the student to complete the exercise depends upon the ability to start with full lungs and continue with only the teensiest amount of exhalation--much like holding one's breath. This exercise gives students a completely incorrect concept of what a real emergency ascent, whether CESA or buoyant ascent, is really like. Most importantly, it gives them the mistaken notion that they can only do it from the shallowest of depths.
In contrast, the 1958 film says that the British navy had done these ascents from more than 300 feet. I have only met a few people who have done true CESAs from depths greater than 75 feet, and each told me that once they started to exhale, there was no stopping it until they reached the surface.