It's possible, especially with roses grafted (joined) on to different rootstock, that if the rootstock was a white rose and more vigorous than the pink rose that it has taken over.
To establish this, see if you can identify where the graft is (should be just above or below soil level) then see whether the shoots are being produced above or below the graft. If from below the graft it is from the rootstock and they need to be removed as close to where they start as possible.
Hopefully enough of the plant above the graft will have survived and you should be able to rejuvenate it.
If the shoots carrying the white flowers are coming from above the graft then I'm at a loss to explain.

Rogerbee's explanation is the most likely, so if its not that, it could just be reversion, if the rose is a fairly new introduction, and particularly if its a David Austen one.