It's probably Clematis terniflora.

We are in Pennsylvania, zone 6 (just outside of Philadelphia). Can anyone tell me if this is an invasive species that should be avoided? I'm kind of seeing things to that effect as I research, but also see that it may just be invasive in more southern locations. I don't want to end up with something that will take over my garden.

Would need to see details of the leaves to determine if this is SAC (C. terniflora) or a similar native species. While SAC is not yet considered invasive in New England, it does have the ability to produce a lot of seedlings, which may become a nuisance. It is also a big, aggressive vine, easily reaching 25-30 feet, so be prepared to allow it considerable space if you do plant it.

I'm seeing Clematis Paniculata (Sweet Autumn Clematis) mentioned on sales sites and the flowers pictured appear to fit my picture.

Am I right in assuming that this will grow upwards rather than fall over a wall? I have a retaining wall that I'm looking for something to spill over it. If I don't give it a trellis to climb up, will it spread along the ground? Will it be hard to control that way?

The leaves ID it as Clematis terniflora AKA paniculata, sweet Autumn. C. virginiana has 3-part leaves. Terniflora is a problem in many areas because it seeds around prolifically, both in your yard and surrounding areas. In my neck of the woods, it doesn't seem to have time to ripen seeds, but in many areas (and I think you are far enough south) it is a problem, ranging from being a nuisance to being outright invasive.

Thanks for the clarification, GG. I think that quite often Sweet Autumn is mislabeled in catalogues as paniculata, so I appreciate knowing that it isn't a synonym for terniflora.

Thank you to all for your answers. This has been a good lesson.