This is called proliferation. Cells in the center of the rose are "malfunctioning" and producing new growth instead of the reproductive parts. The reason is not quite clear. There are many statements that a period of cold in spring can induce such growth, but this is not proven. Here is an explanation from the website of Apuldram Roses:

https://apuldramroses.wordpress.com/2012/05/21/rose-proliferation/

We have had it in our garden with 'Asta von Parpart' where 99 out of 100 blooms proliferated! There are reports of this phemonen since the 1760's, the rose called in England 'Childing Provence' (as it produces children) or 'Rosa provincialis prolifera'. Redouté painted a well-known picture of this rose:

http://rudolfshistorischer-rosen-park.blogspot.com/2013/07/spiele-de-natur-proliferation.html

I suspect that the gene structure of Centifolias has elements which encourages proliferation from time-to-time. Remember that also "moss" started on centifolias. With centifolias then being hybridized into further classes, this tendency apparently got distributed further. It is relatively seldom with repeating roses, and only with the first flush.

What to do? Some break off the proliferated buds so that the strength of the rose is not lost on "deformed blooms". With once-blooming roses, this may of course mean that you loose that year's bloom. The reports I have seen are that usually the following year's bloom has no proliferation. We did part part, left some as curiosity and broke off others.