Car is running fine, gets normal mpg, has normal power, no CEL, but it sounds a little dieselly - grumbly. Car has 86k, original injectors, recent spark plug change, recent air filter change, just changed the oil.
People describing their cars as "sounding like a diesel" generally have one of two problems - if it's a clatter from the rear of the head, it's a cam chain tensioner. If it's more of a rumble, it's an exhaust leak, usually from a torn flex joint.
Two ways to approach flex pipe repair. The "official" VW way is to replace the entire segment of the exhaust that contains it (it's welded in). Cost and details vary depending on the car, but non-trivial. The smart way is to have an exhaust shop cut it out, and weld in a generic ($30-$40) part, Total job is usually under $200.
I had a similar noise. I thought it was the tensioner for the accessory belt, but it turned out to be the skidplate had shifted or warped enough to intermittently rub against the belt. Freaked me out but it was a quick fix.