Officers received a report of a 26-year-old man being the victim of a serious sexual assault in the Ainslie Park area of Pilton, in the early hours of Monday morning.
But in a statement issued today, police said: "Following the report of a serious sexual assault in the Pilton area of Edinburgh in the early hours on Monday 28 October, detectives have carried out a thorough investigation and inquiries have concluded, with no criminality established.
"No further police action is required.
“Officers would like to thank the public for their cooperation to allow investigations to take place."
Meanwhile, a 42-year-old woman was taken to hospital after being seriously hurt following an attack on Monday morning.
The woman was discovered inside a common stairwell at an address on West Pilton Avenue, at about 5:25am yesterday.
Police have appealed for witnesses to come forward.