Actually, I was wondering about that too. So I went and looked at Twilight again and figured I'd drop you a comment.

Apparantly, Esme jumped off the cliff but didn't die straight away. She was taken to the hospital morgue because the hospital staff knew there was no hope for her; she was alive but barely. Carlisle went to the morgue for... some random reason (:D), and found Esme, her heart still miraculously beating.

And VOILA!! Instant vampire, just add venom :D

I hope that helped. <3