Generative Shape Reconstruction with Geometry-Guided Langevin Dynamics

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.