ZODIAC: Zero-shot Octree-based Diffusion for Anatomical Completion

Recovering the full 3D spine anatomy from intraoperative ultrasound is an ill-posed inverse problem, as the complete structure must be inferred from incomplete and noisy observations. Acoustic occlusions and limited field of view create large unobserved regions, while view-dependent artifacts lead to variability in expert annotations of the visible anatomy. Current supervised ultrasound shape completion methods rely on synthetically generated incomplete-complete paired data to learn conditional mappings under a predefined distribution of simulated occlusions. However, real intraoperative occlusions do not necessarily follow this distribution, which can limit generalization to patient data. As a result, accurate and robust completion from noisy partial observations remains an unsolved problem. We propose a zero-shot shape completion framework that reconstructs the entire lumbar spine from partial ultrasound observations without relying on simulated training data. To accommodate unseen and irregular patterns of missing structures, we introduce blended completion, a mechanism that integrates the learned anatomical prior with incoming partial geometry at inference time. The method learns a generative diffusion prior over full anatomical shapes represented in an adaptive octree structure, enabling efficient modeling of the complete spine in a single forward pass. Validation on phantom and volunteer data shows that decoupling completion from a predefined corruption distribution improves generalisation under real occlusions, outperforming a fully supervised variant by 22% on HD95 completion error. Code and data are available at https://github.com/miruna20/ZODIAC.