Depends on the noise. Something can be loose or worn. With the limited info I have, check the catalytic exhaust shields, they tend to rust and break off and hang.
It sound like something dragging or some. Someone said it could be swing band.
Or transmission mount
Looking for a Used CTS in your area?
CarGurus has 13,116 nationwide CTS listings starting at $1,000.
Search Cadillac CTS Questions
Cadillac CTS Experts