How is a stator like a diverging passage? I've read in a lot of places that stators in an axial compressor are responsible for diffusing air and removing the radial velocity to make the flow parallel to the shaft. What I don't understand is how this is accomplished. One way I've heard it explained is this:


  With these fundamental points in mind, let us consider the energy transfer between the moving blades and the fluid. For this discussion, consider an axial-flow compressor with such a large ratio of hub diameter to tip diameter that the blades may be approximated by a linear cascade, that is, an infinite row of blades moving in a straight line, as at the top of figure 5.1. If we were to follow an element of fluid as it passed through the moving rotor, we would note changes in both its velocity and its pressure. The character of the changes is more easily seen by transforming to a coordinate system stationary in the rotor, where the flow seems steady, but from an angle as shown by the dashed vectors. If the blades are shaped to turn the flow toward the axis in this coordinate system (in the direction of blade motion), they form diverging passages which (for subsonic flow) result in rising pressure as the fluid passes through the cascade. When this pressure increase is carried back to the stationary coordinate system, as we see from equation 5.5, energy is added to the flow.


Source: Aircraft Engines and Gas Turbines (2nd Edition) by Jack L. Kerrebrock)

Can someone explain in more detail how a stator is like a diverging passage (diffuser?) as Kerrebrock proposes?

An explanation I would propose (but would appreciate confirmation for) is that there is a pressure gradient along the axial flow due to the rotor/stator's generating lift giving them a suction side upstream and a pressure side downstream. This pressure gradient would cause the flow to slow down (and hence increase pressure). Right?
If you take a look at the geometry of the path between two stator blades and compare the cross section of the path(relative to the direction of the traveling gas), you can see, that they form a divergent path.