Divorce

You can start the process while you are still living together, however, you need to be living in separate households (or have agreed that you will be) when the actual constat is signed.

I know a couple who have been divorced for over two years and who still live in the same house.
They jointly own the house but neither can buy the other out and , if it is sold, neither will be able to buy a new place, so they are stuck with living separately but under the same roof. Extremely awkward but, presumably, legal.
In any case, any notaris will answer such a question quickly and without charge.

How the process works will depend on 1) whether you and your partner can come to an agreement on any financial settlement between the two of you and 2) any custody arrangements for children. Assuming the the two of you can agree on the above, the the actual legal process of getting divorced is actually extremely simple. You draw up an agreement, and you are called to present yourself before a judge twice over the followng 6 months to confirm that you want to get divorced. That's it.

You should go and speak to a notaire.

There is a very comprehensive website covering the issues here:
http://www.notaire.be/divorce-separation/

You should be aware that, in principal, you have to divorce in the country where you last lived together as man and wife - presumably Belgium in your case - but your divorce in one EU country will be recognised in all the others.
My wife tried to divorce her ex in her country - where they married and where she was, by then, living with me but could not because they had later moved to his country and were still there when the marriage broke down.