I recently purchased a 2008 Audi A4 S-line 3.2 with a broken chain tensioner and bent valves as a project to fix and make some money (this is my 3rd Audi fix). The previous owner said it had been sitting for almost a year before I bought it. I replaced the cylinder head and tensioner and got everything back together. Upon starting, white smoke almost immediately poured out of each exhaust pipe. The engine, however, sounded and behaved fine. I let it sit for a week. The next week, I performed a compression test and found all cylinders to have reasonable compression: 110-120 psi. I let the car idle for 15 minutes and monitored the coolant: no apparent loss. The smoke was not as bad as previously, but still apparent. I drove the vehicle and it ran fine with no CELs on. When I next started it, no smoke appeared on startup and during idle, however, on acceleration the smoke quickly billowed out. Currently there is almost no smoke during idle, but large amounts during acceleration.

In summary: white smoke is billowing out of both exhaust pipes on acceleration. The coolant level is not going down. The cylinders all have decent compression. The oil level is fine. No engine codes.
What could be causing this smoke?? I am thinking it could be transmission fluid, unfortunately no easy way to test fluid level that I know of. Or maybe the smoke was caused by sitting and will go away after some run time?

Thanks in advance.