Category-level 6D pose and shape estimation requires recovering an object's pose and geometry from partial observations without an exact instance model. We present ASM-6D, which couples generative complete-geometry prediction with explicit category-level pose-shape inference through shared correspondences. Given an RGB-D image, ASM-6D generates alternative complete 3D correspondence hypotheses whose point identities are shared with a category-level Active Shape Model (ASM), including occluded points. Each hypothesis is fitted directly for rotation, translation, metric scale, and instance shape without a separate correspondence-assignment stage. We analytically eliminate translation and shape coefficients, reducing fitting to a nine-variable scaled-rotation optimization problem that enables efficient batched evaluation of multiple hypotheses in real time. ASM-6D achieves state-of-the-art performance on ROPE and HouseCat6D benchmarks. Ablations demonstrate the importance of generative correspondence prediction and active shape variation. The representation also supports shape completion, shape-dependent pose ambiguity, tracking, and robotic grasping at 6-38 Hz, depending on the inference budget.

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