Short answer : "No, your DPS won't change based on the difficulty level of the current game"
Your DPS in directly related to the base damage of your weapon(s). The DPS calculation can indeed be simplified as this :
DPS = Base Damage * Damage Modifier(s)
Damage modifiers are skill and stat dependants, but have the same effect, they will apply a boost coefficient to your base damage. As an exemple, 1 point in your primary stat will give you 1% damage increase.
Thus, increasing the base damage when changing your weapon(s) will result in a huge increase of your DPS.
For example, let's assume you're a Demon Hunter and have 500 dexterity, which gives a +500% base damage increase.
- With a 100 DPS weapon, you'll get
DPS = 100 * (1 + 500/100) = 600
- With a 200 DPS weapon, you'll get
DPS = 200 * (1 + 500/100) = 1200
Given that some armageddon weapon give you 1000+ dps and you can reach very high scores in your primary stat (not counting other bonuses as attack speed, damage bonus, ...), you'll see that your DPS can get to really high scores.
See this related question for more information on how DPS is calculated.