What is the meaning of the butterfly?

In the movie The Door (org.: Die Tür) there are repeated ocurrances of a butterfly. First of all David's daughter Leonie wants to go catching butterflies when her father doesn't have time for her and when she finally drowns in the pool. Later it is a butterfly that leads David to the eponymous door to the past. And at the end of the movie, when future David and Maja sit at the pool in the past, we see the butterfly fly away, I think.

So does the butterfly have any special meaning in the movie, and what could that be? Given that the movie is about time travel and correcting your past errors, I had to think about the Butterfly Effect, both the movie and the theoretical concept it was based on. But that interpretation doesn't hold too strong I think, given that the movie wasn't so much about the future consequences of changes to the past and didn't involve any feedback of past changes to David's or anybody else's future at all.