This doesn't sound like a good idea.
A classmate working in the same company where I will start in September is planning to renegotiate his salary after graduation.
Never base your decisions on someone else's thought process. Give it a thought keeping your own personal position 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 wait till the end of your trial period/next appraisal cycle. You have recently interviewed with the company. Completion of diploma won't be a new knowledge for the company (most likely you are hired condition to the successful completion of your diploma). 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.