Separated parents want to bring dates

My parents split up about 18 months ago, and do not see or speak to each other at all. They have both asked me if they can bring dates to the wedding, and I am really not sure if I want either of them to. Neither is seeing anyone at all, they just want to bring someone (a friend, I guess) so they don't have to be by themselves. I don't think it's too unreasonable for them to want that, I just don't know how comfortable I am with the idea.

Anyone else in this situation? How did you handle it?

I just want to clarify - if either of my parents was seeing someone, I would not hesitate to tell them to bring the person. But I feel weird about them 'finding' a person to go with.

My mom asked me about it about 6 months ago and I told her exactly what I just said - if she's seeing someone at the time, yes. But I don't see the need in dragging some random person to my wedding.

My dad asked me about it today. He has a couple of people he thinks he would ask, and he said it might make him feel more comfortable if he had someone to talk to.

I don't know, maybe I just feel so weird about it because I really want the two of them to be sitting together and talking and dancing. Not likely to happen, though