# UBone3D: Physics-Rectified Conditional Flow Matching for Anatomical 3D Shape Completion from Ultrasound

arXiv: https://arxiv.org/abs/2609.11506 · HTML: https://mlsanity.com/paper/2609.11506/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 49 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 30 of 33)

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [GRNet: Gridding Residual Network for Dense Point Cloud Completion](https://mlsanity.com/paper/2006.03761/) (2020)
- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [PhysTwin: Physics-Informed Reconstruction and Simulation of Deformable Objects from Videos](https://mlsanity.com/paper/2503.17973/) (2025)
- [SeedFormer: Patch Seeds based Point Cloud Completion with Upsample Transformer](https://mlsanity.com/paper/2207.10315/) (2022)
- [Optimal Flow Matching: Learning Straight Trajectories in Just One Step](https://mlsanity.com/paper/2403.13117/) (2024)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [CTSpine1K: A Large-Scale Dataset for Spinal Vertebrae Segmentation in Computed Tomography](https://mlsanity.com/paper/2105.14711/) (2021)
- [ProxyFormer: Proxy Alignment Assisted Point Cloud Completion with Missing Part Sensitive Transformer](https://mlsanity.com/paper/2302.14435/) (2023)
- [PhysAnimator: Physics-Guided Generative Cartoon Animation](https://mlsanity.com/paper/2501.16550/) (2025)
- [SVDFormer: Complementing Point Cloud via Self-view Augmentation and Self-structure Dual-generator](https://mlsanity.com/paper/2307.08492/) (2023)
- [Ultra-NeRF: Neural Radiance Fields for Ultrasound Imaging](https://mlsanity.com/paper/2301.10520/) (2023)
- [SuperPC: A Single Diffusion Model for Point Cloud Completion, Upsampling, Denoising, and Colorization](https://mlsanity.com/paper/2503.14558/) (2025)
- [PCDreamer: Point Cloud Completion Through Multi-view Diffusion Priors](https://mlsanity.com/paper/2411.19036/) (2024)
- [Neural Implicit Surface Reconstruction of Freehand 3D Ultrasound Volume with Geometric Constraints](https://mlsanity.com/paper/2401.05915/) (2024)
- [DMF-Net: Image-Guided Point Cloud Completion with Dual-Channel Modality Fusion and Shape-Aware Upsampling Transformer](https://mlsanity.com/paper/2406.17319/) (2024)
- [RoCoSDF: Row-Column Scanned Neural Signed Distance Fields for Freehand 3D Ultrasound Imaging Shape Reconstruction](https://mlsanity.com/paper/2408.07325/) (2024)
- [Rethinking Multimodal Point Cloud Completion: A Completion-by-Correction Perspective](https://mlsanity.com/paper/2511.12170/) (2025)
- [Shape Completion in the Dark: Completing Vertebrae Morphology from 3D Ultrasound](https://mlsanity.com/paper/2404.07668/) (2024)

## Abstract (arXiv)

Three-dimensional ultrasound (US) is a safe, radiation-free complementary modality to CT and X-rays for longitudinal monitoring, yet its segmentation-derived partial point clouds are extremely artifact-laden. Consequently, it is challenging to recover a clean and complete anatomical structure from such US point clouds. In this paper, we present UBone3D, a novel framework based on physics-rectified conditional flow matching (CFM) that performs point cloud completion directly from partial US observations. UBone3D models deterministic physics artifacts (e.g., surface thickening, streaking, dropouts) via a simulated physics proxy, and introduces test-time physics rectification to steer the shape completion. At inference, the completion is jointly steered by two decoupled forces: (1) anatomical plausibility enforced by a CT-trained generative shape prior, BoneFM, and (2) physics consistency enforced by USimNet in the ultrasound formation space. Extensive experiments on simulated and in-vivo data demonstrate significant improvements in reconstruction accuracy and anatomical fidelity over existing baselines.