# Generative Shape Reconstruction with Geometry-Guided Langevin Dynamics

arXiv: https://arxiv.org/abs/2603.27016 · HTML: https://mlsanity.com/paper/2603.27016/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 49 of its 59 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 30 of 49)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Objaverse: A Universe of Annotated 3D Objects](https://mlsanity.com/paper/2212.08051/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Objaverse-XL: A Universe of 10M+ 3D Objects](https://mlsanity.com/paper/2307.05663/) (2023)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [CLAY: A Controllable Large-scale Generative Model for Creating High-quality 3D Assets](https://mlsanity.com/paper/2406.13897/) (2024)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [Hunyuan3D 2.0: Scaling Diffusion Models for High Resolution Textured 3D Assets Generation](https://mlsanity.com/paper/2501.12202/) (2025)
- [Michelangelo: Conditional 3D Shape Generation based on Shape-Image-Text Aligned Latent Representation](https://mlsanity.com/paper/2306.17115/) (2023)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [TripoSG: High-Fidelity 3D Shape Synthesis using Large-Scale Rectified Flow Models](https://mlsanity.com/paper/2502.06608/) (2025)
- [AutoSDF: Shape Priors for 3D Completion, Reconstruction and Generation](https://mlsanity.com/paper/2203.09516/) (2022)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Dora: Sampling and Benchmarking for 3D Shape Variational Auto-Encoders](https://mlsanity.com/paper/2412.17808/) (2024)
- [3DILG: Irregular Latent Grids for 3D Generative Modeling](https://mlsanity.com/paper/2205.13914/) (2022)

## Abstract (arXiv)

Reconstructing complete 3D shapes from incomplete or noisy observations is a fundamentally ill-posed problem that requires balancing measurement consistency with shape plausibility. Existing methods for shape reconstruction can achieve strong geometric fidelity in ideal conditions but fail under realistic conditions with incomplete measurements or noise. At the same time, recent generative models for 3D shapes can synthesize highly realistic and detailed shapes but fail to be consistent with observed measurements. In this work, we introduce GG-Langevin: Geometry-Guided Langevin dynamics, a probabilistic approach that unifies these complementary perspectives. By traversing the trajectories of Langevin dynamics induced by a diffusion model, while preserving measurement consistency at every step, we generatively reconstruct shapes that fit both the measurements and the data-informed prior. We demonstrate through extensive experiments that GG-Langevin achieves higher geometric accuracy and greater robustness to missing data than existing methods for surface reconstruction.