Following reports of a disturbance, police were called to Granton Square at around 1.10am.
Two men, aged 19 and 21, were found with serious injuries and taken to Edinburgh Royal Infirmary to be treated.
Detective Sergeant Dougal Begg, said: “These men received serious injuries and therefore it is imperative that we establish exactly how they came about them.
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“We are currently carrying out enquiries, however would appeal for anyone with any information to come forward.
“Passing taxis or private hire vehicles in the area may also have dash-cam footage that could be vital in our enquiry. We would urge you to get in touch.”
Anyone with any information should contact Police via 101, quoting incident number 0261 of Saturday, 3 July, 2021.
Alternatively you can contact CRIMESTOPPERS on 0800 555 111.