The incidents in Castle Park, in Bristol city centre, happened between 30 November and 5 December, Avon and Somerset Police said on Wednesday.
A man in his 30s was treated in hospital after being struck on the head in the most recent incident, the force said.
A 32-year-old man has been arrested on suspicion of assault in connection with the incident, and released on police bail.
The attacks began when a man in his 40s was hit on the head after being approached by two unidentified men who shone a light in his eyes at around 1.15am on 30 November.
He suffered injuries to his wrist, back, shoulder and head.
Two reports of similar incidents were made in the early hours of 3 December, between 12.30am and 1.30am.
The victims, aged in their 20s and 40s, are not believed to have needed medical treatment for their injuries.
A spokesman for the force, speaking about the attacks, said “officers are concerned they may be homophobic in nature”.
He said descriptions of the suspects were limited due to the time of night, but they are believed to be two males – one white – who were wearing face coverings and dark clothing.
Members of the public are urged to remain “vigilant” in the area after dark, he said.
Detective Inspector Alistair Norman, who is leading the investigation into the “concerning incidents”, said that while detectives are “open-minded” about the investigation and the motivation for the assaults, they “are currently treating these incidents as linked”.
CCTV footage has been examined while interviews, and local inquiries have taken place.
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Chief Inspector John Shaddick said: “We understand this update will be distressing for members of our community. There is no place for hate crime in our city, and we will not tolerate such behaviour.
“We are taking matters of public safety in and around Castle Park, and the wider city centre, very seriously”, he said, including consulting with local LGBTQ+ leaders.
“We have implemented a number of measures, including the use of our mounted team, dog units and increased regular foot patrols, to enhance visibility, engagement and to deter further criminal activity.”
