Originally this piece was called "Love and Pain". It was only later that it picked up the name "Vampire" and interpretation of a man locked in a vampire's embrace. Munch maintained it was nothing more than a woman kissing a man on the neck.
Personally, I don't like either interpretation. I see a man in emotional pain, and a woman comforting someone she loves. Her hair is carelessly draped over him, covering him from the outside, as if he ran like a boy seeking his mother. Instead, his lover suffices. And she knows just by the look on his face that this is what he needed. They are so familiar, even this bizarre circumstance is met with understanding and concern. She doesn't ask what is troubling him, she knows it is dreadful, imagining the horrible details.
The Nazis declared it morally 'degenerate.' Some thought it was about his visits to prostitutes, yet others saw it as some sort of macabre fantasy about the death of his favorite sister. Evidently Munch remained ambiguous about the deeper meaning behind it.