The album features eight new compositions by Halvorson, performed with her sextet Amaryllis; the improvisatory band that performed on her critically praised 2022 albums Amaryllis and Belladonna comprises Halvorson, Patricia Brennan (vibraphone), Nick Dunston (bass), Tomas Fujiwara (drums), Jacob Garchik (trombone), and Adam O'Farrill (trumpet). Labelmate Laurie Anderson also is featured on the album track "Incarnadine."All the music on Cloudward was written in 2022, mostly in the fall and winter, when things started moving forward. Life felt like a creaky machine starting up again," she continues. "Air travel, however chaotic, had resumed, and we were once again cloudward. Performances and tours and recordings were happening after a long hiatus and with a renewed sense of gratitude. This band, for me, was quite simply working, both musically and personally, and the main thing I felt while writing the music was optimism."