It's pretty much all Handsome Furs songs, with one song that's new to me called “ Floating World,” which I couldn't seem to find anywhere.
Adult World (2013) SoundTracks on IMDb: Memorable quotes and exchanges from movies, TV series and more Floating World Written by Dan Boeckner.
The Tale of the Floating World (2002). 24min | Animation, Short, Drama | January 2002 Hiroyuki as an adult. Takuji Suzuki Samurai. Kazuhiro Nakahara.