Are there any factors that influence loot quality?

Solution 1:

Here are the things that I know for sure affect loot drop quality

• Difficulty level. A map on hard is going to have better quality loot. Not just from the harder monsters but chests as well.
• The Map (i.e. the later maps drops better stuff, glitterhelm on hard drops way better stuff than deepest depth on hard).

Here is what I think affects it (can't confirm for sure)

• Maximum available character levels in the game. I.e. a game of all level 70s tend to see better loot than 1 level 70 and 3 newbies with level 10 characters.

The boss rewards do have a higher chance of dropping a better quality item on higher difficulties.

As for challenge maps, most challenges give different rewards based on difficulty level but those rewards are unaffected by character level.

Solution 2:

In addition to what yx mentioned, loot also seems to get better the map wave number is. A hard survival game in wave 1 will drop worse loot than that same game on wave 15.