Rihanna On the Mend -- Pregnant Rumors Persist

Rihanna came out of a medical building in Bev Hills Tuesday ... and said she's doing a lot better, but it's done nothing to stop the pregnancy talk.

Rihanna has cancelled 4 concert dates on her Diamonds World Tour ... which kicked off on March 8.

Sources connected to the singer told TMZ in early March she was suffering from a throat infection. Thing is ... it's been more than a month now and there are clearly still issues.

Because the info coming from Rihanna's camp has been sketchy ... there have been a slew of tabloid stories speculating that she's pregnant.