This plant is growing in the woods and along the highway in Tennessee. I have also seen it in Ohio. All of the plants I have seen are 10' or shorter and have opposite leaves.
Yes, does look like it comes from that genus. To help narrow down to the species attached is a picture of the leaf stem. It is hollow and the sap smells bitter sweet.
http://plants.usda.gov/java/profile?symbol=PATO2 P. tomentosa seems to be the only species reported to have escaped cultivation. HTH Chris
Have pruned the lower branches of our Paulownia tomentosa and can confirm that the stems are hollow. Leaves look identical to your photos. In the U.K. the flower buds are already well formed on the tree, ready for next spring. Over here its common name is "Foxglove tree".
OK, thank you all! I read on one site it was spread to the U.S. from the seeds being used as packing peanuts for shipping china abroad.