A woman in her 20s was sitting at a bus stop in Scotland Road when a man sat next to her and touched her inappropriately shortly before 3.25am on June 28.
The victim jumped up from her seat, prompting the man to quickly leave the scene.
Officers say the victim managed to flag down a passing police car for assistance.
Police are now urging anyone who may have any information that may help them with their enquiries to get in touch.
T/DS Ash Johnston, of East CID, said: “This was a very distressing incident for the victim and she is now being supported by specially-trained officers.
"We are appealing for witnesses who may have seen the suspect in the area at the time or anyone with CCTV or dashcam footage to get in contact.”
The suspect is described as an Asian male, aged between 25 and 35-years-old, with dark black hair and short dark facial hair.
He was wearing a black jacket and black jogger pants, according to police.
Anybody with information should contact police by calling 101, quoting log number 0228 of June 28.
Alternatively, independent charity Crimestoppers can be contacted anonymously on 0800 555111 or via their website https://crimestoppers-uk.org/