Passiflora arida is invasive at least in Arizona.
It has been misidentified as Passiflora foetida.

http://www.azgfd.gov/w_c/edits/documents/Passariz.d.pdf
excerpt:
"AIDS TO IDENTIFICATION: Passiflora arizonica is the only Passiflora found in Arizona with a lilac-colored corona and pinnatifid stipules. It is easy to distinguish from a commonly confused naturalized (and invasive) species of Passiflora in Arizona, P. arida. P. arida lacks the obvious glandular trichomes that are so abundant in P. arizonica, and generally has more numerous, longer and narrower leaf lobes than P. arizonica."

Note that Passiflora foetida variety arizonica has been recently reclassified as Passiflora arizonica. A real nice plant and I'm told the fruits taste good.

More on recent reclassification and invasiveness at
http://www.cababstractsplus.org/google/abstract.asp?AcNo=20043057022
"Abstract: Two species of Passiflora in Arizona (USA) and northwestern Mexico are investigated. One species, P. arida, native to Baja California and Sonora, has recently been found to be naturalizing in southern Arizona. Another, P. foetida var. arizonica, native to southern Arizona and Sonora, is examined for taxonomic distinctiveness and raised to a new species, Passiflora arizonica. These two species are compared to each other, the potential threat of weediness in P. arida is reviewed, and the distinctive features of the biology of P. arizonica are discussed. Furthermore, comparisons are made with several other related New World Passiflora species of similar geographic range or morphology."