"  A perfect example of jazz improvisation" Theories of what constitute improvisation in music may be helpful. But listening to great examples of this art form makes it emotionally available.You may  be familiar with Debussy;s Clair De Lune from his Suite Bergamasque. Pianist Fred Hersch begins by playing the composition as written and as we know it. Then he takes off in a magical , accelerated flight of fancy. We now hear aspects of the basic melody but augmented by what Hersch feels inspired him to build on the original, creating a new composition of his own,
In fact, much of classical music uses theme and variation tropes. Rachmaninoff's Rhapsody on a Theme of Paganini contains 18 different treatments of the original theme. 

https://youtu.be/wEMWZM3k_q0