Movies that this film references/copies..
Kramer vs. Kramer - The poster, theme, design, Adam driver's haircut and clothes (Dustin Hoffman), the baroque music, New York street scenes, the name of the kid was Henry (Justin Henry was the kid in Kramer). The similarities to Kramer vs. Kramer are endless.
Ingar Bergman films, especially Fanny and Alexander which this film copies shot by shot in the bed scene. Take a look:
Marriage Story: https://i.ytimg.com/vi/emaUIZWKiWM/maxresdefault.jpg
Fanny and Alexander: http://magicofstory.com/wp-content/uploads/2019/01/Fanny-and-Alexander-e1546388213584.jpg
Also Scenes from a Marriage (1973).
All that Jazz (1979) - The theater scenes in the beginning and the Adam Driver singing at the end.
Did I miss anything?
Great film by the way. Even though it was inspired by the films above -- Noah made it into his own film.