Here we are actually using some of those inversions to play 2 5 1’s all over the neck. This is an example in F but try it in all 12 keys! The chords are Gm7b5 — C7b9 — Fm7.
The diminished function is a C7b9 without the root. To look at a C7 chord we have
C — E — G — Bb
Flat nine would be Db
Diminished we’re using is built
G — Bb — C#(Db) — E
As you can see the diminished has all the notes of the C7b9 but the C. Hey! Isn’t that what bass players are for?! (kidding 😉 )