European almonds from seed? Will I get bitter or sweet almonds?

I have a beautiful almond tree which was sold to me by a nursery as a sweet almond. It bears heavily, but sadly the almonds are extremely bitter. I believe this can happen with a percentage of European almond trees. I read that it's about 10%.
I wonder about planting some of the seeds, but does anyone know what the genetics are?  If the parent tree is bitter, will it always have bitter offspring or is there a chance I can get a sweet almond tree among the seedlings?
I'm assuming it's self-pollinating as there are no other almond or peach trees nearby.