We aim to solve the problem of data-driven collision-distance estimation given 3-dimensional (3D) geometries. Conventional algorithms suffer from low accuracy due to their reliance on limited representations, such as point clouds. In contrast, our previous graph-based model, GraphDistNet, achieves high accuracy using edge information but incurs higher message-passing costs with growing graph size, limiting its applicability to 3D geometries. To overcome these challenges, we propose GDN-R, a novel 3D graph-based estimation network.GDN-R employs a layer-wise probabilistic graph-rewiring algorithm leveraging the differentiable Gumbel-top-K relaxation. Our method accurately infers minimum distances through iterative graph rewiring and updating relevant embeddings. The probabilistic rewiring enables fast and robust embedding with respect to unforeseen categories of geometries. Through 41,412 random benchmark tasks with 150 pairs of 3D objects, we show GDN-R outperforms state-of-the-art baseline methods in terms of accuracy and generalizability. We also show that the proposed rewiring improves the update performance reducing the size of the estimation model. We finally show its batch prediction and auto-differentiation capabilities for trajectory optimization in both simulated and real-world scenarios.

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