The robberies were all carried out during the early hours of Tuesday, June 12, and detectives say they have already made “numerous enquiries” to identify those involved.
A 24-year-old man was attacked from behind in the first incident, which took place in Dortmund Square at about 12.30am.
He was punched and had his phone stolen before his attackers made off along Mark Lane.
In the second incident, a 23-year-old man was set upon in Regent Street at about 1.15am.
He was kicked several times before the suspects took his jacket and ran off towards Leeds Playhouse and Ludgate Hill.
Another 23-year-old man suffered head injuries in the third incident, which happened on Navigation Walk near Bridge End at about 1.40am.
His attackers stole personal property and then made off towards Crown Point Road.
Leeds District Crime Team’s PC Chris Atkins said: “These were cowardly and quite vicious attacks on individuals simply going about their business.
“We will not accept this type of behaviour on our streets and we are doing all we can to trace those responsible and bring them to justice.
“To assist in our enquiries, we have taken the step of releasing images of four men, who we would urgently like to speak to in connection with this series of offences.
“At the times these robberies occurred, there will have been few people on the street and someone may have remembered seeing some unusual or suspicious activity.
“If you have any information that could assist in our investigations or know the whereabouts of the men contained within these images, I would urge you to get in touch.”
Anyone with information is asked to ring West Yorkshire Police on 101 or Crimestoppers anonymously on 0800 555111.