I wrote about this weed in my December 31, 08 SF Chronicle column, Golden Gate Gardener. Tried to give you a link, but will need some help from the blog administrator to do it. I can tell you that you can see the article at sfgate.com, click on "Living", then "more Home and Garden," then "Golden Gate Gardener."
But no, the flowers give it away. This plant is related to Dicentra, bleeding heart. It is called Fumaria capreolata, or white ramping fumitory. To ramp is to climb up, which it does by tendrils. (You can see a forked tendril on the lower right.) It climbs all through other plants and if you pull on it, it breaks, so you have to reach down through your garden plant and find the base, so you can pull it by the root. It's an annual plant only, so pulling it will kill it, but if it drops its seds, then you will have it next year, and for several more, probably. It's kind of pretty in a closeup, but when you see a whole mass of it, it is untidy and kind of nondescript.
I have been working hard on a writing project recently, but plan to get back to blogging now, at least once a week. I have photos of what has been happening in the City College garden and will be posting them and writing about them. Stay posted for more postings.