How do the flowers of Diphylleia grayi become transparent after rain?
I have to hypthesise here:

the white colour you perceive is most likely near-to-full diffusion (or possibly better phrased: reflection with effectively undirected refraction due to multiple reflections) of light by structures on the surface of the petals and/or air space encapsulated in the petals. (This is true for most white flowers, by the way.)

Water fills the structures and/or the air space, which changes the refractive index of the petal surface. 

In other words: the flower becomes like water, because the air is driven out.

Edit: seems I was right. SE asked me to add links to my answer, so I asked GoogleScholar about D. grayi and found this: "The inner part of the petal comprises numerous lacunae and intercellular spaces that are filled with air."
(source: Yong et al. (2015). Bioinspired transparent underwater superoleophobic and anti-oil surfaces. Journal of Materials Chemistry A, 3(18), 9379-9384.)