My reading indicates that without a qualifier, it covers all diseases, even magical ones, like mummy rot (which are also curses). Unless there is a qualifier or modification in the specific wording of the creature, it looks like it's just immune to disease.
Having said that, there are things that seem unusual in that case, like the creature being able to Treat Disease with a +12 Heal modifier on itself. It works on others, it's just unusual that they specify that it can do it on itself, which is weird if it's immune. But by the wording on Immunities and the FAQ answers on being immune to disease and whether it applies to magic diseases (unless the disease specifically says otherwise), it seems to be immune to even magical or supernatural diseases.
If I’m immune to disease, am I immune to mummy rot, which is both a curse and a disease?Yes.
Note, that there is a 'magic-resistant' version of diseases. These can apply to creature with disease immunity. AfflictionsThere are also things that fall under 'disease effect' or can be removed by spells and effects that cure disease but which I might allow to affect this creature. For example, I don't think I'd make it immune to an infestation (like fleas or something), though it certainly wouldn't necessarily take damage or effects as a normal creature (effectively becoming a carrier). That's just my view on the specific case, though.