Duplicate songs in iTunes

I've had an iTunes library for more than 15 years, filled with more than 1,000 albums either purchased from iTunes or imported from CDs. I also have iTunes Share to listen to all my music across my devices. I recently signed up for Apple Music, and I've just noticed that certain -- not all -- albums have each song duplicated. It seems very random. Within the purchased or imported album on iTunes, each song appears twice with one version of each song with the download badge next to it. This is extremely annoying. Is there some setting that I'm missing to turn this off?