Generate injective functions with QuickCheck?

I'm using QuickCheck to generate arbitrary functions, and I'd like to generate arbitrary injective functions (i.e. f a == f b if and only if a == b).

I thought I had it figured out:

newtype Injective = Injective (Fun Word Char) deriving Show

instance Arbitrary Injective where
  arbitrary = fmap Injective fun
    where
      fun :: Gen (Fun Word Char)
      fun = do
        a <- arbitrary
        b <- arbitrary
        arbitrary `suchThat` \(Fn f) ->
          (f a /= f b) || (a == b)

But I'm seeing cases where the generated function maps distinct inputs to the same output.

What I want:

• f such that for all inputs a and b, either f a does not equal f b or a equals b.

What I think I have:

• f such that there exist inputs a and b where either f a does not equal f b or a equals b.

How can I fix this?