MDIS has foundation cert in biological science, then after completing it, you may do a diploma in biomedical science then do a degree in biomedical science. However, you cannot practise as a doctor. It is more for life science research.
Do check out MDIS or even PSB websites.
All the best.
There's no such thing as a "private medical diploma".
To be a doctor, you need a degree from the list of recognised universities
http://www.doctors.com.sg/medicalschools.html
UtimaOnline is right.