I just watched this movie and had no idea who wrote the music as I watched it. At first the score reminded me of Carter Burwell's lyrical cues from "In Bruges," then other times it brought to mind Desplat's "Coco Before Chanel," so I wasn't surprised to see in the closing credits that it was by Desplat. It's quite lovely, and I re-watched big chunks of the film just to sample some of that music again.
So it was disheartening to read here that there isn't a soundtrack CD. I'll try to find some of it online.
Addendum: Couldn't find any of it ANYWHERE. And apparently Desplat himself has said that there won't be a soundtrack release. Drat!