The pair had been enjoying a night out at the Starbank Inn in Newhaven before being subjected to the attack, which police say was unprovoked.
Officers are keen to trace four suspects who had been drinking in the same pub just before the incident.
The incident started when a 34-year-old man was attacked by one of the group of four men near the Laverockbank Road premises at around 1am on May 31.
His companion, a 28-year-old woman, tried to intervene – but the three other suspects then got involved in the attack, and she was knocked unconscious. The four attackers – believed to be three men and a woman – then fled the scene, leaving their victims on the pavement.
It is understood that the two victims initially declined medical help after the incident, but went to the doctor several days later because they were in so much pain.
Both of them suffered facial fractures and other injuries, and the incident is being treated as a serious assault by police.
Officers are now appealing for witnesses to come forward to aid the investigation.
They have released descriptions of the four suspects and they also want to trace a taxi driver whom they believe may have witnessed the assault.
The three male suspects are all described as being in their 30s and 40s, while the woman is believed to be around 5ft 6in tall, with a medium build.
She had long dark hair and was wearing a black jacket at the time of the assault.
The first man is described as 5ft 10in with a medium build, a shaved head and a distinctive heart tattoo with a keyhole on his right forearm.
The second suspect is around 5ft 11in with a heavy build, short dark hair and was wearing a dark jacket, while the third man was of a slim build, 5ft 10in tall and wearing a light-coloured shirt.
Detective Sergeant Clark Martin, who is leading the investigation, said: “This was a seemingly unprovoked and brutal attack and we are eager to trace anyone who may have witnessed the incident, or has any information which can help with our inquiries.
“We’re also eager to speak to a taxi driver seen in the area at the time of the assault, who may be able to help with our investigations.”
Anyone with information is urged to contact Police Scotland on 101 or contact anonymous hotline Crimestoppers on 0800 555 111.