PABLO Picasso must be smiling in his grave – a great, orgasmic grin of pleasure at the fact that, 80 years after he painted his young lover, Marie Therese Walter, the portrait still has the capacity to shock.

Last week, several passengers arriving at Edinburgh Airport were sufficiently disturbed by a poster showing the portrait, Nude Woman In A Red Armchair, to complain, prompting managers to cover up the offending image, which was advertising the Gallery of Modern Art's latest exhibition.

National Galleries director general John Leighton reacted swiftly, branding the airport's action "bizarre" and describing the painting as a "joyous and affectionate portrait of one of Picasso's favourite models".

But perhaps those Edinburgh Airport complainers were on to something. After all, what is absent from Leighton's description is the fact that this work is clearly and blatantly about sex. A firm, white breast hovers, like a target, in the centre of the image, and below is the outline of what appears to be a hairless pudendum. To suggest that this is not about sex would sanitise and disempower the work. Joyous it may be – but it is so in the manner of a smiling, pneumatic Playboy pin-up who appears to want nothing more than to give her flesh to the viewer. When Picasso met Walter, he was 45 and married to Olga Koklova. Walter was 17 and would bear his child several years later.

Certainly, this portrait is "affectionate", but a flip side to its sweetness can be found in the dark, seemingly misogynistic contemporaneous portraits Picasso made of his wife, Olga. Once one knows this context, it is impossible to see the bouncing, vibrant images of Walter as simply sweet. Let us remember that this is an artist who once said that there were two types of women, "goddesses and doormats".

It is not only prudes who might find the Nude Woman In A Red Chair difficult to deal with, but also anyone who is uncomfortable with the continuing notion that the acme of femininity is submissive availability. Walter was, according to Picasso's biographer, "exceedingly submissive, infinitely sustaining, and no fool".

Her yielding, voluptuous passivity is conveyed in the painting. And today, when despite feminist progress, Page Three hotties offer a fantasy of submissive availability and the best-selling book, Fifty Shades Of Grey, deals in sadomasochistic fantasy, there is still something disturbing about this paean to female surrender.

Should a work like this be censored within a public space? Arguably, the same standards should apply for art as for all other advertising. And if, as happened last year, an M&S advert of a woman in knickers and bra can be banned, it is hard to see how this one should be spared, except by saying the anotomical part depicted "doesn't look real". One of the odd things about our culture is that we have evolved different, more permissive rules for art. Leighton pointed out: "It is obviously bizarre that all kinds of images of women in various states of dress and undress can be used in contemporary advertising without comment, but somehow a painted nude by one of the world's most famous artists is found to be disturbing and has to be removed." But do we really see images like this, genitals uncovered, on billboards throughout the country?

It is hard to know what Picasso would make of today's surfeit of semi-pornographic imagery. But given that there are still so many taboos around sex and the body, there is no doubt he would have still found ways to shock us. A 1972 exhibition of Picasso's erotic engravings was dismissed as the senile scrawlings of a dirty old man.

Two years ago, curator Jean-Jacques Lebel drew together an exhibition called Picasso Erotique. He knew Picasso's enduring power to shock and at the time he said he wasn't even going to try to take the show to the United States because of what he deemed "cultural censorship". Among the exhibited works was a 1956 image in which Picasso drew himself onto a magazine page as a lascivious old man sizing up a pin-up model. It is worth bearing this in mind when we look at the Walter portrait, remembering that this is a man who seduced this young woman when she was almost 30 years his junior.

Not that these works are pornography. It's hard to imagine anyone using the stylistic, fractured form of a Picasso nude as pornographic inspiration. Indeed, Lebel argues that Picasso's more erotic works have "nothing to do with pornography". Rather, he points out, the artist "is asking the question, what is this thing called Eros, and how does it link to painting?" Similarly, Picasso biographer John Richardson has said women were central to Picasso's work and life because he "was always apt to associate sex with art: the procreative act with the creative act".

Perhaps the National Galleries knew what it was doing when it chose Walter as its poster girl. Indeed, I wouldn't be surprised if the censorship episode turned out to be a publicity stunt. We all know sex sells. And the painting itself is, as Leighton points out, one of Picasso's more "joyous" ones. It is the kind of feelgood sex that really does seduce. But the problem is that, these days, few still believe in that simple, happy vision of female sexual availability and bounty.

Those who know the story behind the Walter portrait, of a woman who was always the mistress not the wife, who killed herself not long after the artist's death, who said she "always cried with Picasso" and "bowed my head in front of him", may feel uncomfortable with it. Just as those who look at Marilyn Monroe's early calendar pin-up shots, with all their breezy joy, can't help but feel there is something more desperate and dark behind the invitations to fun. In other words, just because a painting is joyous, doesn't mean that it can't be difficult, threatening and even offensive.

But of course, the National Galleries well knows that.