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Manipulating volumetric deformable objects in the real world, like plush toys and pizza dough, brings substantial challenges due to infinite shape variations, non-rigid motions, and partial observability. We introduce ACID, an action-conditional visual dynamics model for volumetric deformable objects based on structured implicit neural representations. ACID integrates two new techniques: implicit representations for action-conditional dynamics and geodesics-based contrastive learning. To represent deformable dynamics from partial RGB-D observations, we learn implicit representations of occupancy and flow-based forward dynamics. To accurately identify state change under large non-rigid deformations, we learn a correspondence embedding field through a novel geodesics-based contrastive loss. To evaluate our approach, we develop a simulation framework for manipulating complex deformable shapes in …