To me, improvising is like speaking a language spontaneously, whereas only reading music and re-creating the music others (or yourself) have written is like reading a book or a story out loud. The reading is scripted, whereas the spontaneous use of language flows where it will, especially if it’s in conversation with another. If you’re new to improvising, it’s a simple thing to do.
Several months ago I spoke with the fantastic jazz trumpeter Ingrid Jensen about practice. She mentioned that one thing she liked to do was practice with drones, using an Indian instrument called a tanpura (also tampura). She said that playing against a drone was a great way to train your ear/horn coordination. Practicing with a drone allows you to really feel how it sounds to play every note against the tonic, throughout your range. It’s meditative.
When I hear a great practice idea, I try it, and I’ve been using this one for a while and absolutely love it. I almost immediately noticed a greater ability to match pitch (my fellow musicians mentioned it in rehearsal), and a deeper awareness of sound in general. Part of the reason for this is that playing with the drone makes me aware of where the horn is naturally out of tune, whether because of the way a horn is made or because of the quirks of the harmonic series.