There are basically three approaches to improvising on jazz standards: melodic paraphrasing, improvising with the harmony, and motivic development which may overlap the previous two.
Agreat many jazz musicians approach the harmonic implications in three ways: harmonic specificity, harmonic generalization, or ignoring harmonic implications.

Harmonic Specificity: Careful attention to implications of harmony. Reliance on proper thirds, sevenths resolving appropriately. Adhering to alterations called for by the chord symbols or melodic implications of the composition.

Harmonic Generalization: Rather than deal with the specifics of the implied harmony, reliance on blues ideas and scales. In the instance of a ii V progression, it is often generalized as a I chord. For example: with the progression
| Dmi7 | G7 | C major 7 |
the C major triad or C major blues is used for the entire phrase.

Ignoring the implications: This can be the result of the improvised line following the direction of motivic based improvisation; the improviser choosing to impose alternate harmony over pre-existing harmony; the improviser choosing to create tension by deliberately playing notes foreign to the implied harmony.

Experienced jazz plays move in and out of the above areas. They are always able to play harmonically specific, and often after being general or vague they will return to the specifics. When an experienced jazz improviser plays deliberately vague, he does so knowing the harmonic implication and therefore what tones to avoid.

Sorry for posting that, I thought it was sort of interesting, but I guess it's irrelevant.

I followed you over here in hopes you left it up. I thought it interesting - thanks for the insight!

Very true - as a way of conceptualising what improvising is. Yet, knowing this, has not helped me learn to improvise.

thanks for posting.