Definitions of the word “improvise” include “to compose, play, recite, or sing on the spur of the moment, without previous preparation” and “to make, provide, or arrange from whatever materials are readily available.”
One of the elements of creativity tests such as the widely used Torrance Test of Creative Thinking is questions about “unusual uses” – such as, “How many uses can you think of for a tin can?”
That sounds like a cognitive sort of improvisation.
You can see drawings by children and adults who took the Torrance Test, plus evaluations by creativity scholars James C. Kaufman and Kyung Hee Kim, in the post How Creative Are You?
The photo is Keith Jarrett. His Amazon.com page lists his albums and notes he “has come to be recognized as one of the most creative musicians of our times – universally acclaimed as an improviser of unsurpassed genius.”