Generative Shape Reconstruction with Geometry-Guided Langevin Dynamics

2026-03-27

AI Summary

Reconstructing complete 3D shapes from incomplete or noisy observations is an ill-posed inverse problem that requires balancing data consistency with the plausibility of shape priors. This work proposes a geometry-guided Langevin dynamics approach that explicitly embeds geometric constraints into each step of the diffusion process, enabling high-fidelity reconstruction by jointly preserving observation consistency and leveraging generative priors. By deeply integrating geometric constraints into the diffusion sampling trajectory, the method uniquely unifies the strengths of data-driven fitting and generative modeling. Experimental results demonstrate that, across various missing-data and noise scenarios, the proposed approach significantly outperforms existing methods in both geometric accuracy and robustness.

Abstract

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.

Problem

• 3D shape reconstruction
• incomplete observations
• noisy data
• shape plausibility
• measurement consistency

Innovation

• Geometry-Guided Langevin Dynamics
• Generative Shape Reconstruction
• Diffusion Models
• Measurement Consistency
• 3D Shape Prior