This looks like powdery mildew. This has become a bigger problem on peonies the past few years. Make sure there is adequate sunlight and good air circulation to reduce humidity levels. Allow proper plant spacing for the same reasons. Pruning for better air circulation also may help. Practice good sanitation.
Cut down all infected foliage now and dispose of. Next spring, monitor your peonies, and as soon as you see one infected leaf, pull it off. You will have to decide it you want to spray a fungicide or a horticultural oil labeled for powdery mildew or tolerate it. Fungicides are preventative--not curative. They will halt further infection, but cannot restore infected leaves to health. There are no resistant peony varieties on powdery mildew. Here is our website info on powdery mildew