When creating a custom filter using the 'Generic'->'Convolution Matrix', the resulting filter has a bias toward darker colors.

A simple way to demonstrate this is to create a new small image (e.g. 100x100) and fill it with 50% gray. Draw a small white square near the top left corner of the image and a small black square near the bottom right corner. Then, make a rectangular selection whose corners are in the middle of the small squares.
Then, create this simple diffusion filter in the Convolution Matrix dialog:
1 1 1
1 0 1
1 1 1
And either use a divisor of 8, or enable 'Normalise'.
Then, apply this filter repeatedly (to get a true diffusion, you'd need to do it an infinite amount of times, but 100 times will be more than enough).

The correct image would show an equal influence of the white corner as for the dark corner, with the center pixel of the image at 50% gray.
In the output from the GIMP, though:
  http://homes.esat.kuleuven.be/~athomas/tmp/gimp_convol_bug.png
the influence of the dark corner completely overwhelms the influence of the white corner and the center pixel is at 30%. The result is the same when the squares are placed in different corners, so it is definitely an effect of intensity, not location. If I'd have to guess the cause, it's probably a rounding error or incorrect bias value somewhere.

If this sounds like an artificial test, I use this technique often to 'inpaint' missing parts in images. This bug makes GIMP useless for this.

I notice the same effect when using the 'blur' tool. Someone else has made a movie which illustrates this: http://schalken.wubbles.net/gimpblurdarkensbug2.ogg