Question: I was going through annual HR training, and one thing jumped out at me. In the "diversity" section, an advice was given to the effect of "if you care about diversity, volunteer to participate in efforts... such as mentor someone".

Now, I have mentored people before, and see it as a wonderful opportunity to both help someone, and learn myself, and strengthen the company.

**But in this context, it seems to be Catch-22**!

* If I approach someone from a diverse background offering to mentor them, that singles them out and seems to *imply that they need mentoring*, which is kind of the opposite of the message that ought to be delivered and promotes less equal treatment environment.
* But if I don't, it's well known that people who would most benefit from mentoring tend to be shyer, and **are less likely to approach someone more senior and ask to be mentored**.

How can this catch-22 be resolved in a productive and appropriate way?

Answer: 
Target someone who is struggling. That is the only way to avoid coming across as condescending and paternalistic. You have correctly identified the catch 22.

I have several disabilities. From my perspective, I would consider it highly offensive if someone were to decide to mentor me simply because I have these problems. However, if I were struggling and the difficulties were related to my situation, I would welcome the help.

THAT is how you make the distinction.

If the person needs mentoring due to their situation, then it's a green light, if not, then you can get into a good deal of trouble.
I find it odd that some of the answers/comments and somewhat the implication of this question is that mentoring is done to help people who are deficient in their skills. Mentoring is generally, in my experience, done to help people you think are capable of being promoted to higher level of responsibility and not the people you think are deficient at their current level. When someone is deficient, that is job training.

Mentoring is generally best done when it arises naturally. Mentor people who work for you or that you have reason to be in professional contact with anyway and don't exclude minorities or women from that mentoring. But don't exclude all white men either. 

Don't go up to someone and say I want to mentor you. Pretty much anyone would find that offputting. Just start to provide advice as it is appropriate to the situation. Be someone who readily answers questions and is approachable. Then let people approach you for advice. In casual discussions start to talk about workplace issues of concern at a higher level than the person is to start to give them the senior perspective. I have mentored lots of people through the years, I have never once had to say to them, "Hey, let me mentor you."