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Manipulating deformable objects requires reasoning about shape, contact forces, local compliance, friction, and uncertainty. Vision-based shape servoing can reconstruct and control the visible deformation of soft objects, and online FEM can extend this estimate to occluded regions. Nevertheless, vision-based perception alone does not observe the local contact mechanics at the grasp or along the robot body. These hidden conditions often determine the task outcome: a similar visible shape may arise from different stiffness distributions, contact conditions, incipient slip, or force distributions. This thesis develops a tactile-informed, uncertainty-aware framework for dual-arm manipulation of deformable objects, in which a physical belief state provides the interface between model-based estimation, safe control, and generative decision-making. A central scientific question is which physical quantities are identifiable from ...