The diopside structure has nothing to do with perovskites at all. Diopside belongs to the clinopyroxenes and these are classified as inosilicates (i.e. silicates with a chain structure of Si a sometimes Al containing tetrahedra). Ideally, it is a salt of the highly hypothetical silicic acid H4Si2O6. Phase structures need to be approached in the opposite way. The most important thing is the actual structural arrangement, the summary formula is a completely secondary matter.

There are a number of programs for plotting crystal structures, and there are also structural data for most phases. The differences are clearly visible in the pictures.

The defining feature in this classification scheme is not the chemical composition, but the topology of the coordination polyhedra. In perovskites, one type of cation is in octahedral coordination by the anions, these octahedra are connected into a cube by shared corners, and the second cation is inside this cube. Diopside structure type is utterly different; the silicon is in tetragonal coordination by oxygen.

thanks for the exhaustive answers

however, it should be noted that the CaSiO3 MaSiO3 compounds have perovskite structures

Neither CaSiO3 (wollastonite) nor MgSiO3 (enstatite) are definitely not perovskites. Like diopside, it belongs to silicates with a chain arrangement of tetrahedra (inosilicates).

Perovskitová struktura je znázorněna bridgmanitem, který je vysokotlakým polymorfem MgSiO3. Existuje také podobný vysokotlaký polymof FeSiO3, nazývaný hiroseit. Oba jsou známy pouze z meteoritů. Vysokotlaký CaSiO3 pravděpodobně také existuje, ale není jasně prokázán.