Precisely manipulating objects in a single photograph (translation, rotation, scaling) while obeying 3D physical constraints remains unsolved for diffusion-based editors. Current 2D methods lack spatial awareness and produce perspective violations. Forcing structural proxies into the latent space also disrupts variance homogeneity, and the resulting self-attention leakage leads to ghosting and background blur. The core difficulty is asymmetric: the relocated object must follow a rigid geometry, yet the uncovered background needs freedom to synthesize plausible content. We present GeoEdit, a training-free Lift-Manipulate-Render-Denoise pipeline that satisfies both constraints. We decouple scene and object in 3D, align them through point correspondence, and render a geometry-aligned proxy with a structural depth map. A Dual-Branch Denoising stage then refines this proxy: a video diffusion backbone preserves object identity, while 3D constraints are injected into the foreground within a narrow denoising window at matching noise variance (variance-homogeneous injection). The background denoises freely. Because the injected signal matches the native latent statistics, self-attention stays undisturbed. We also introduce GeoEditBench, a pose-aware benchmark covering object translation, object rotation, and camera movement with pose-aware evaluation metrics. Experiments confirm consistent gains in geometric accuracy, identity fidelity, and background quality. Our codes are available at https://github.com/Heey731/GeoEdit.

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