Recently I was infected when I engaged some bloodfiends in the Rift. I got the popup message alerting me. I went to the priest in Elden Root to talk to him but did NOT pay him to cure me. Afterwards, I periodically saw the red mist effect (I think it shows when you log in, and maybe come through a wayshrine), and it showed in my status effect.
Yesterday, I noticed that I hadn't seen the mist effect in a bit, and when I checked my status effects, the disease was gone.
Does it go away if you don't continue the quest line (I forgot there was one/didn't know how to continue it anyway)?