There are many films that celebrate psychoanalysis, reflecting the popularity of various forms of psychotherapy in Hollywood. From Home of the Brave and Now Voyager in the 1940s through to the early oeuvre of Woody Allen and Ordinary People, analysis has generally been shown positively (though you do get the odd evil or incompetent psychologists in horror films like Dressed to Kill or Cat People).

A Dangerous Method, a remarkable, important, if flawed, film directed by David Cronenberg, and based on the play of the same name by Christopher Hampton, does something new. It explores the people who gave birth to psychoanalysis and modern psychology. It is a somewhat talky costume drama, especially by the standards of Cronenberg, whose previous work is dominated by kinky but clever science fiction and horror. But, after an awkward, unsubtle start it does a creditable and provocative job of bringing to life Carl Jung, Sigmund Freud, and the less well-known but fascinating figure of Sabina Spielrein, Jung's patient and possible mistress, who became a protégée of Freud and then a psychologist of considerable note.

Unfortunately, Knightly adopts a strange German-American accent as the Russian-Jewish Sabina, and Viggo Mortensen as Freud adopts a creditable English accent: as so often, the effort adversely affects their performances.

Moreover, Knightly almost wrecks the film in the first 15 minutes. Actors love playing mad people, and Knightly goes embarrassingly over the top with strange insect-like body movements as a young woman being dragged forcibly to the Zurich clinic where young Dr Jung (Michael Fassbender) is experimenting with Freud's talking cure in 1906.

Spielrein, it turns out, is tortured with self-loathing because of the pleasure she took as a little girl from frequent beatings by an abusive father. She is also brilliant and Jung soon has her working with him as part of her cure. With his wealthy, adoring wife pregnant at home, it is only a matter of time before his relationship with the highly sexed Sabina evolves into an affair.

The film includes an episode in which the eccentric, drug-addicted analyst Otto Gross is sent to Jung's establishment, where, like an ambassador from late 20th-century Hollywood, he gets to lecture Jung on the advantages of a sexually self-indulgent life without repression or restraint. The fine French actor Vincent Cassel does a terrific job with Gross, making him simultaneously sympathetic and repellent.

Mortensen's buttoned-up Freud comes across as difficult and egotistical, with a blind spot about his patriarchal urges and the Oedipal nature of the struggle with Jung, his protégé turned rival. There is something flat and mannered in the performance as if his famously in-depth research has leeched life out of it

The film is scrupulously fair in its depiction of the early struggles in psychoanalysis. It is hard to tell where Hampton and Cronenberg stand on Freud's unbending insistence that sexual urges are at the root of all neurosis or on Jung's attraction to mysticism.

It may not be entirely true that Freud's perceived "betrayal" by Jung made him more suspicious of gentiles as is implied here, but it does seem to be the case that Jung was powerfully attracted to Jewish mistresses as well as to what was known as "the Jewish science".

However, for a movie that clearly prides itself on historical accuracy, one of its flaws is that all of the cast are far too film-star thin to be convincing as early 20th-century Mittel-Europeans. When Knightly's Sabina is dragged into the clinic, her protruding clavicles make you wonder if she is being treated for anorexia rather than hysteria.