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Human-like generalization in open-world remains a fundamental challenge for robotic manipulation. Existing learning-based methods, including reinforcement learning, imitation learning, and vision-language-action-models (VLAs), often struggle with novel tasks and unseen environments. Another promising direction is to explore generalizable representations that capture fine-grained spatial and geometric relations for open-world manipulation. While large-language-model (LLMs) and vision-language-model (VLMs) provide strong semantic reasoning based on language or annotated 2D representations, their limited 3D awareness restricts their applicability to fine-grained manipulation. To address this, we propose LAMP, which lifts image-editing as 3D priors to extract inter-object 3D transformations as continuous, geometry-aware representations. Our key insight is that image-editing inherently encodes rich 2D spatial cues, and lifting these implicit cues into 3D transformations provides fine-grained and accurate guidance for open-world manipulation. Extensive experiments demonstrate that \codename delivers precise 3D transformations and achieves strong zero-shot generalization in open-world manipulation. Project page: this https URL.