The 19-year-old female was grabbed by a man and dragged into a garden area in Salisbury Place, in the south of the city, at about 2.50am on Sunday.
The woman managed to fight off the attacker, who made off towards Minto Street.
The man is described as white, in his early 30s, 6ft and of large build with dark hair. He was wearing a red kilt, calf-high boots and a dark hooded top with numbers on the front.
Officers believe the man visited the Marchmont Takeway on Marchmont Road some time between 7pm and 9pm on Saturday before walking along Newington Road towards Salisbury Place.
Detective Inspector Donnie MacLeod said: “Since the attack took place we have been conducting various inquiries in and around Salisbury Place to trace witnesses and establish the movements of the suspect before and after the incident.
“We are now satisfied that he was within the Marchmont area on Saturday evening before carrying out the attack, during which time he walked towards Salisbury Place from the direction of the city centre.
“I would ask anyone who believes they may have seen this individual on Saturday night, or the early hours of Sunday morning, or who knows where we can find him, to contact police immediately.
“In addition, anyone with any further information relevant to this investigation is also asked to get in touch.”
Inspector Graeme Nisbet added: “I would like to stress that incidents such as this are extremely rare, not only in the south side, but across Edinburgh.
“Nevertheless, we recognise the impact this has had not only on the victim, but the local community, and we have increased our visibility in the area through dedicated and high-visibility patrols.”
Anyone with information can contact police on 101 or alternatively Crimestoppers on 0800 555 111 where information can be given anonymously.
Local councillor Cameron Rose is also urging any residents with any information to come forward as soon as possible.
Detective Inspector Donnie MacLeod, from the Public Protection Unit at Fettes Police Station, said: “This was a terrifying ordeal for the young woman.
“Thankfully she was able to fight her attacker off before running away.
“We have already spoken to a number of witnesses but I would urge any other members of the public who remember seeing any suspicious activity within the Salisbury Place area during the early hours of Sunday morning to contact police immediately.
“I would also ask anyone who recognises the description of the suspect to also get in touch.”
Minto Street is one of the city’s busiest thoroughfares and has a large student population, with Edinburgh University close by.
Anyone who believes they may have information about the attack, can contact Police Scotland on 101 or alternatively, the charity Crimestoppers on 0800 555 111 anonymously.