Amanda Cox was reported missing at around 3pm on Monday from the Edinburgh Royal Infirmary in the Little France area of the city.
Police said she was last seen in her pyjamas and slippers.
The 34-year-old was discovered collapsed within the Edinburgh Royal Infirmary just hours later at around 10pm.
She sadly passed away a short time later.
It is understood Amanda had given birth just a matter of days prior to her disappearance.
The death is being treated as unexplained, but not suspicious.
Police Scotland said a ‘sudden death’ report was being prepared for the Procurator Fiscal in Edinburgh and a full post mortem examination would be carried out to determine the cause of death.
A Fatal Accident Inquiry into the tragedy may be ordered by the Crown Office.
A police source said: “There was nothing apparent that would suggest this is anything other than the tragic death of a new mother who had recently given birth.
“She was found within the hospital and obviously there will be aspects of the investigation that will look into the seven hours she was unaccounted for until she was found.”
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