I guess that would be subjective to some degree - i.e., would you consider self-defense or the physical defense of your loved ones "violence" if provoked and you were required to physically hurt someone to stop them from hurting you or your loved ones? Personally, I would not. Violence to me would be unprovoked attacks or physically acting first when unnecessary as a defensive posture. So I guess in short, based on the above, no. I don't think love demands violence, unless you define it differently than I do. As for the question of love always being positive or not - I would say yes. Could there be pain involved in love, absolutely, but generally that pain helps a person grow/evolve emotionally and ultimately, in my experience, becomes a net-positive.

These are just the opinions of one man, me, I'm sure many others will have different opinions.