A 39-year-old man was attacked at about 03:30 on 24 September 2016 in South Clerk Street.
The victim was knocked to the ground and was seriously injured.
Officers said the men had been seen near the attack and were with two young women. Anyone who recognises them is asked to come forward.
Police Scotland said they were particularly interested in speaking to the man shown in the centre of the image.
He had dark hair and a larger build, was about 5ft 9in tall and was about 18 or 19 years old. He was wearing a grey sweatshirt.
Det Sgt Adam Brown said: "This was an unprovoked assault which resulted in the victim sustaining an injury with a protracted recovery period and has significantly disrupted his daily life since.
"Anyone who recognises any of the males or who witnessed the assault is urged to get in touch as soon as possible."
Police have released CCTV images of three men they want to trace over a serious assault in the centre of Edinburgh.