> A classmate working in the same company where I will start in September is planning to renegotiate his salary after graduation.

Don't base your decisions on someone else's thought process. Give it a thought keeping your own personal situation in mind.

> Do you think I can make the same request, or would it be better to wait until the end of the trial period?

It's better to end till the end your trial period/next appraisal cycle. You have only recently interviewed with the company. Your completion of diploma won't be new knowledge for the company (in-fact it is what company may be waiting for before you start with them). So this is not a skill/certificate that you are acquiring out of company's knowledge which adds value to your role.

Even if you are thinking along the lines of re-negotiating, it will sound good only if you are brining in new skills to the table that aligns with role.

Given the situation, it's best to prove your mettle by showing your work and negotiate a deserving pay with confidence in the next cycle.