The 24-year-old was walking on a footpath linking Gillespie Road to West Mill Road in Colinton when the man launched the daylight assault.
Detectives are investigating whether the attack may have had a sexual element, but are currently treating the motive as “unascertained”.
The man did not utter a word as he tried to haul the woman into an isolated patch of woodland during the incident at around 2.10pm on Thursday.
The attacker only released the victim after he spotted a couple walking along the footpath about 50 metres away and fled the scene.
The victim, who suffered bruising and swelling to her face, did not require hospital treatment but was left “badly shaken” by her ordeal.
Detective Sergeant Kevin Harkins, from Corstorphine police station, is leading the inquiry. He said: “The victim was walking along the Water of Leith walkway when she was approached by this man who was running towards her. She was punched twice in the face by the man who then grabbed hold of her.
“The man tried to drag her over a wall into a wooded area, but he was frightened off by a man and a woman walking along the footpath.
“We are not ruling out a sexual motive to this attack, but the motive is currently being treated as unascertained.
“We are not linking this attack to any other incidents at present. It seems to have been an isolated assault.”
The suspect is described as white, late 20s, more than 6ft tall, with a stocky build and heavy stubble. He was wearing a black hooded top with the hood over a blue baseball cap, blue jeans, and white trainers with a blue stripe on them.
DS Harkins added: “We are keen to speak to the couple who disturbed this man. They may have been in their 50s or 60s and possibly wearing dark waterproof clothing. They were about 50 metres away when he fled so they might not have heard the victim shouting.
“It’s an area popular with dog walkers and others so we are appealing to anyone who may have seen this man in the area to come forward.”