Jasmine was a woman with whom Cauchemar fell in love.
After being separated, he found the colony world where she had settled. He had gone through an area of space with severe radiation and was dying. He tried to use genetic material from her to repair himself, but she was injured in the process. He took her to the Creator in hopes of her being healed, but she was killed instead.
He spent years looking for her reincarnated spirit, and thought she found it in Treena Grace. He killed her when he believe Jasmine's soul was in Treena's sister Ettianne instead. (PROSE: Vanishing Point)