These turbos have vayable geometry vanes which act as nozzles optimizing exhaust flow and pressure to the turbine, minimizing turbo lag.

Can similar variable geometry be used in the compressor side...the diffuser?

Masochist to Sadist: "Hurt me."
Sadist to Masochist: "No."

The short answer is "yes". For most applications the additional complexity of using both isn't justified. If it were, the turbo could be kept operating at higher efficiencies across a broader engine speed and load range. That's not a common requirement.
Controlling turbo speed is easier on the "power-input" side than on the "load" side.