These photographs were taken by me, all on the same day (June 10th), from around two in the afternoon till maybe nine at night. The flower's common name is NIGHT BLOOMING CEREUS. The link takes you to the Wikipedia entry on the plant's family, which includes this flowering species as well as the one that produces DRAGONFRUIT. The botanical name of this particular plant is most likely Epiphyllum oxypetalum, or Gooseneck cactus. The related variety, cultivated for the fruit, is called Hylocerus undatus.
I wrote a blog entry about this some years ago, because I was totally blown away to discover that there was any kind of link between this beautiful and very short-lived flower and the fruit -- perhaps because I associate the fruit with Southeast Asia, having eaten it for the first (and only) time in Singapore. Most people who have seen or know of the flower do not associate it with the fruit AT ALL. But if you compare the strangely zoological appearance of the flower's bud, it is easy to recognize the shadow of the fruit's shape in it.
The flower doesn't last the night and by morning, it looks like a pale pink bat-carcase. My sister got her plant from a friend who said they had never seen the flower blooming but had heard it was spectacular. In my sister's house, it has bloomed so often it's like a regular cabaret! Sometimes a dozen blossoms will all go critical in the same night. She says they don't bloom very often, but more than once a year.