With a concave profile the aim is to obtain a more abrupt deceleration in the very first part, near the throat/leading edge, getting closer to the maximum ideal pressure recovery, coherently with the energy of the boundary layer, which is in fact achieved when the b.l. itself is constantly kept at limit of separation.
The same theory is valid not only for diffusers, but for the deceleration area of airfoils too (obviously, the aim is the same...), google for Liebeck airfoils to see a practical application of the concept.
The problem is that, exactly because the maximum pressure recovery demands pushing the b.l. to limit of separation, it's a potentially more critical design that operates optimally in a rather limited range of conditions and dramatically loses efficacy at the minimal variation, and that makes often preferable a more conservative convex profile, that induces a more limited peak deceleration the b.l. is more easily able to cope with, sacrificing pressure recovery in favor of versatility.
That presumably explains the difference we see in F1 diffusers, with the central, narrow, part typically convex, while lateral channels are concave.
In the middle the floor gets quite close to the ground, so the area at the throat is small and changes greatly with small variations of ride height, and geometry is not particularly favorable being narrow and open at the sides, things making more difficult to control the flow thus increasing risk of separation; a smoother transition with a gradual change of slope, imposing a smoother deceleration and keeping the b.l. more distant from limit of separation, is preferable in order to get a more stable behavior for all the working conditions (obviously any trick to improve the situation, like blowing thru the starter hole, energizing the flow, can allow to be more "aggressive" and move a bit towards the ideal)
For the lateral channels, more distant from ground at the throat, thus less sensitive to ride height variations, that problem is lot less evident and they can afford using a more effective profile, concave, closer to the ideal shape for maximum pressure recovery.
BTW, concave profile is nothing new, as you can see in this WT model of Ferrari's F310B (1997) floor, that was on display at Galleria Ferrari in 2005 showing pressure distribution, with distinctly in evidence the peak of pressure localized at the kink: