It is normal during growth stage. Pay attention to moisture, but do not overwater - peonies do not like wet feet.

I have this happened to a few of my peonies this year. Some snapped out of it and bloomed very well and some did not. The ones that did not had all the buds blasted and had no flower. I am not sure whether the roots were somehow affected by tree roots competition or just the late cold causing root damage.

No, true' peonies do not like 'wet feet', but they don't like to dry out, either. How deep are the roots? Remember peonies like their tubers to be shallow; but this means that they dry out more quickly too... My peony did this in my old garden; I watered them and kept the soil moist and then they recovered....

This happened to me last year and the year before. My Angel Cheeks peony came up and the leaves were all curled up. I ended up moving away some of the mulch that I had covering the area and viola! The pant grew in much nicer and the leaves were no longer curly. I dont think they like being covered too much.

thanks for your replies
all of my peonies were purchased last spring.
planted all of them on my front lawn at first then these 2 were moved to my backyard later in the summer... I wonder if it's because it was moved...
it has flower buds but tiny... one opened yesterday and was very small.
I'm guessing if it's because I moved it, would it be back to normal next year?
size comparison, the one on top
thank you

If you moved them so soon after planting, in my opinion you're lucky to actually have any blooms at all! Peonies are notoriously fickle and fussy when it comes to depth and movement, so you did well to get any buds at all!

I'm of the view that the move caused the bloom anomaly and providing they're not too deep, you should get something better next year.

Here is an established peony (3rd year) showing sign of leaf curl this past spring. The leaf curl happened as soon as the peony started growing and to bud stage as you can see. The only thing that I found that was different with this year was very mild winter and then followed by a very cold early spring. Some peonies seem to be affected by this. But they go on and bloom very well for me when the weather warmed up and the leaves started to look normal.

I had another peony with the same leaf curl that never recovered. All the buds were blasted and no bloom. The leaves are growing fine now but no blooms eventhough it is also an established peony going on the 3rd year.