During the Cannes Film Festival press conference for the film, Lars von Trier responded to a question about the use of Wagner's music, by calling himself a Nazi, and saying that he sympathized with Hitler. Despite apologizing for his remarks, he was banned from the remainder of the festival, and declared a persona non grata by festival organizers, a first in the history of the festival.
The painting seen in the prologue is Pieter Breughel's Hunters in the Snow (1565). This painting also prominently features in Andrei Tarkovsky's Solaris (1972). Lars von Trier often stated Tarkovskiy greatly inspires him. He even dedicated his previous film, Antichrist (2009), to the Russian director.
The advertisement for which Justine is supposed to come up with a tagline, is based on an oil painting by Pieter Bruegel the Elder titled "The Land of Cockaigne", an unflattering portrayal of excess and spiritual emptiness in a mythical land of plenty.
John Everett Millais' painting "Ophelia" and Pieter Breugel's "The Land of Cockaigne" are referenced in the images of the movie. Moreover, both paintings can be seen in the art books that Justine uses to rearrange the bookshelves in the library.
Justine's text about the loneliness and evilness of the Earth, about to be destroyed, refers to Genesis 6:13. If Justine is right, this may explain the scientific implausibilities of Melancholia's movement towards Earth.
Lars von Trier said he got inspiration by the Nibiru Cataclysm, a possible encounter between Earth and a planetary object. An event also referenced in the Bible (Genesis 6:13), where God said to Noah: "I am going to put an end to all people, for the Earth is filled with violence because of them. I am surely going to destroy both them and the Earth."