Do soul gems scale with level?

With most item types the items you find gradually scale with your level. You might find an iron dagger at level 1, but if you come back after the area/dungeon has been repopulated and you are higher level, it might be an dwarven or ebony dagger. Do soul gems scale in the same way? Are you more likely to find higher tier soul gems as you gain levels (apart from the fact that you are more difficult places)?

Yes, they do. Posted below is a chart of player character levels, and chances of getting specific types of soul gems for each level, depending from the source.

This is from the UESP wiki, "Leveled Lists - Soul Gems"

Note: At each level, an item is added to the list, so at any level there will be the items listed at that level and every prior one on the list. It will then pick one of those randomly. Note that many have multiple entries, making that particular soul gem more likely. A grayed out cell indicates that nothing is added to that particular sublist at that level.

About leveled lists:

Skyrim uses leveled lists primarily to adjust content to the player's level. But they are sometimes used to group objects for other reasons.

^{Source: UESP wiki, "Leveled Lists"}