I am undergoing treatment of diplopia and right now it is fine, but my question is; it could be more serious (partial blindness) in the future?

There are over 30 reasons that can cause this. And there are several types. Only your doctor knows short or long term outlooks, depending on the reason that caused this, how treatment is going and more.

Normally this does not lead to blindness and in many cases treatable. Only your doctor will know