Generating 3D hand-object interactions is essential for applications in robotics, XR, and synthetic data generation, where flexible controllability and strong generalization to diverse object geometries are required. However, existing methods rarely satisfy these requirements, limiting their practical applicability. We present DCGrasp, a distance-aware controllable grasp generation system built on a novel grasp energy term. This term computes Distance Profile, a signed distance from each hand vertex to the nearest object point, coupled with distance-aware weighting, effectively capturing the semantically similar hand-object interaction in near-contact regions while remaining invariant to object and hand identity. Given various controllable signals, DCGrasp first generates a Distance Profile based on a Diffusion Transformer, together with a corresponding candidate hand pose. We then refine the candidate pose through optimization, enforcing consistency between the optimized hand pose and the generated Distance Profile in near-contact regions. Our experiments show that DCGrasp produces high-quality, physically plausible grasps with flexible user control, generalizing to diverse object and hand shapes and scales. Our work establishes a robust and versatile pipeline for the synthesis of controllable 3D hand-object interactions.
Cross-end-effector grasp generation seeks a unified model that generalizes across objects and across embodiments ranging from parallel grippers to dexterous end effectors. Existing grasp generators are typically designed for a fixed embodiment or encode embodiment identity with a static descriptor, which weakens transfer when topology, actuation coupling, and contact geometry differ substantially. We present EAGG, an embodiment-aligned grasp generator that represents each embodiment with a topology-aware end-effector graph and an embodiment-specific low-dimensional end-effector control space. A frozen end-effector-cognition backbone converts the current articulated state into geometry-aware tokens that act as a reusable morphology prior, and iterative geometry injection refreshes these tokens throughout sampling so that conditioning remains synchronized with the evolving end-effector geometry. On the MultiGripperGrasp benchmark, EAGG reaches 56.17% average success across six training end effectors, remaining within 1.10 percentage points of specialized training while preserving transfer to finetuning and zero-shot end effectors. Iterative geometry injection further reduces the pooled median contact distance from 0.239 cm to 0.189 cm. These results show that cross-end-effector grasp generation is strengthened by aligning embodiment structure inside a shared generator rather than suppressing embodiment differences. Code is available at https://github.com/wanhaoniu/EAGG.