Spectrum intensity varies depending on the frequency span
The spectrum analyser is making choices for various things like resolution bandwidth, video bandwidth, number of averages, according to an algorithm decided by the people who specified the instrument firmware. This was to optimise their idea of the SNR/time tradeoff in each offset span.
You need to force the instrument to make your choice of those things if you want visual continuity between the spans. You may be able to do this, it depends whether the firmware gives you that option.
Notice I talk about 'visual continuity' in the previous paragraph. This to point out that this is all you would be doing, prettifying the display. If you want to understand the measurements of the diode under test, then you've a lot more work to do to determine how much noise is from the analyser, how much from the diode, and what the spread of noise on the analyser display is really telling you.
In a way, the display transitions have helped you, by forcing on you that the display needs interpretting.