The painting really does change, but so does Dorian Gray. The painting may age instead of the man himself, but Dorian Gray grows ugly on the inside.
Technically, the painting ages after Dorian pledges his soul, so there is an element of the supernatural in the story, an unspoken deal with the devil, the forces of darkness. Dorian becomes a hedonistic, evil individual and when you see the portrait, and it is hideous, so is the man.
The textual evidence suggests that the portrait does indeed change. When Dorian encounters Basil Hallward on a London street, they discuss the scandalous rumors that surround Dorian, and Basil asks if they are true. In reply, Dorian offers to show Basil "his soul" and takes him to the room where his disfigured portrait is hidden. Basil's reaction to the changed portrait enrages Dorian and drives him to murder the artist. Since someone else sees the portrait, we know that its transformation was not solely in Dorian's mind.
A state of high belief and faith can cause an internal concept to become externally manifest in reality; for example, severe stress can cause marks to appear on the suffers skin, a Communion wafer is thought become the body of Christ, or water to wine. There may be no supernatural source causing the painting to change, rather it is likely the powerful internal suffering of the man that causes the manifestation. This is a question Oscar wants us to painfully ponder, so there is no clear answer; is the cause from without or within? This question, and the story overall, thus reflects back to the soul of the author and his own sufferage.