I wear all sorts of adult diapers in public and very thick ones sometimes as well and no one has noticed anything about me wearing diapers.
However a good absorbent diaper but also thin diaper is Attends Poly backed diapers or Northshore Supreme plastic backed diapers.
Depends Plastic backed diapers which are known as Depends Protection With Tabs is also another good discrete but absorbent diaper for public wearing.