The incident happened around 12.15am on Sunday in Mansfield Avenue, Musselburgh.
A 57-year-old woman was returning home from a night out and had just walked through a vennel when a man approached her.
The man then grabbed hold of her and kissed her before attempting to assault her further. After a struggle the woman was able to flee and contacted police.
Detectives are now urging anyone who can assist with their enquiries to come forward.
The suspect is described as being in his early 20s, 5ft 5ins tall with an olive-skinned complexion, slim build and short dark hair. He was wearing dark clothing.
A police spokesman: “This was an incredibly frightening experience for the victim and we are carrying out local enquiries to identify the man responsible.
“Anyone who was in the Mansfield Avenue area in the early hours of Sunday morning and remembers seeing anything suspicious is asked to contact police immediately.
“Similarly, members of the public who can assist identify the suspect are also asked to get in touch.”
Anyone with any information is asked to contact Lothian and Borders Police on 0131 311 3131 or Crimestoppers in confidence and complete anonymity on 0800 555 111.