cs.CVMar 27, 2026
SaveGenerative Shape Reconstruction with Geometry-Guided Langevin Dynamics
Organizations: Technical University of Munich · Munich Center for Machine Learning
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.
Figures & tables
Figure 1: GG-Langevin. We combine the prior learned by a diffusion model with gradients from a geometric loss at inference time. By guiding the trajectories of Langevin dynamics, we obtain shapes that are both measurement-consistent and prior-consistent.
Figure 2: Blue trajectories: Non-guided Langevin dynamics on the prior distribution , initialized at an incomplete shape using the VAE encoder . It generates plausible, complete shapes but quickly drifts from the measurements. Green trajectory: GG-Langevin generatively reconstructs the shape from the input point cloud. By incorporating gradients from a geometric loss , it keeps the sampling trajectory close to the manifold of measurement-consistent shapes where (indicated by the dashed red line). On the right: A side-by-side comparison of sampling trajectories from Langevin dynamics and Geometry-Guided Langevin dynamics.
Figure 3: Toy example. Demonstration that our method generates samples from the geometry-guided distribution . Blue: Data distribution. Red: Two variants of guidance weight. Green: Geometry-guided product distribution. Solid lines indicate the predicted closed-form distributions. The histograms show samples generated using regular Langevin dynamics and GG-Langevin, respectively. We train an MLP diffusion model on samples from a bimodal Gaussian . The samples closely follow the predicted distributions.
Figure 4: Reconstruction results on sparse point clouds. Provided sparse point cloud scans as input, GG-Langevin recovers the complete surface and fine structures, significantly improving the reconstruction accuracy in comparison to previous work.
| Sparse Scans | Incomplete Scans | ||||||||||||||||
| Cars | Airplanes | Tables | Chairs | Cars | Airplanes | Tables | Chairs | ||||||||||
| CD | CA | CD | CA | CD | CA | CD | CA | CD | CA | CD | CA | CD | CA | CD | CA | ||
| Optimization | IGR [ 18 ] | 1.07 | 27.7 | 2.80 | 33.4 | 2.36 | 25.1 | 2.52 | 29.1 | 4.47 | 32.8 | 3.82 | 31.7 | 6.04 | 29.2 | 5.38 | 30.4 |
| DiffCD [ 20 ] | 1.22 | 29.3 | 0.88 | 25.7 | 1.48 | 21.0 | 1.58 | 24.1 | 5.40 | 33.1 | 3.26 | 28.4 | 6.02 | 23.5 | 5.13 | 26.0 | |
| Learning-based | 3DILG [ 51 ] | 1.68 | 30.6 | 1.01 | 25.9 | 1.37 | 23.1 | 1.38 | 26.7 | 5.50 | 32.4 | 4.40 | 24.3 | 4.80 | 18.2 | 4.51 | 22.8 |
| VecSet [ 52 ] | 1.81 | 32.5 | 0.99 | 26.8 | 1.29 | 17.7 | 1.23 | 22.6 | 5.55 | 36.1 | 3.36 | 23.1 | 5.31 | 18.9 | 4.96 | 23.8 | |
Table 1: Shape reconstruction. Comparison of different methods on ShapeNet categories for sparse and incomplete scans. Lower is better for both Chamfer Distance (CD) and Chamfer Angle (CA) in degrees. We highlight the best-performing method in each object category in bold and the second-best underlined.
Figure 5: Reconstruction results on incomplete point clouds. Despite incomplete point cloud scans as input, GG-Langevin recovers the missing structure with prior-consistent geometry. By comparison, previous work either struggles to complete the geometry or hallucinates implausible completions.
Figure 6: Sampler ablation. Performance comparison of methods for sampling from the geometry-guided distribution shape . We use the same latent space and loss function for all methods. The table on the right shows the Chamfer Distance (CD) and Chamfer Angle (CA) averaged across all object categories.
Figure 7: Impact of noise level and guidance strength on reconstruction performance. If is too small relative to the shape overfits the noise. Conversely, if is too large, the shape starts drifting away from the measurements.
Figure 8: Design choices for the autoencoder. We reduce the size of the decoder while maintaining the overall size of the autoencoder. Further, we predict a full SDF instead of a Truncated SDF (T-SDF) to enable gradients for the geometric prior.
Figure 9: Autoencoder ablation. Reconstruction quality with varying bottleneck position (26 layers total). Using 10 decoder layers balances quality and inference speed.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 10: Failure cases. While rare, failure cases largely fall into two categories: incomplete reconstructions, where part of the shape is missing from the reconstruction, and spurious geometry, where redundant geometry is hallucinated.
Figure 11: Siren weight comparison. Increasing the Siren loss weight, , typically leads to less spurious geometry (top row), but can also lead to incomplete reconstructions (bottom row). The table shows metrics averaged across all shape categories.
Figure 12: Adding class conditioning. Comparing GG-Langevin with and without class conditioning. The class-conditioned model has a clear advantage in the incomplete setting, where predicting the object category from the point cloud is more difficult. In the sparse setting, both models perform similarly. For all our main experiments, we use the unconditioned model, which does not require the class label as input.
Figure 13: Initializing baselines. For a fair comparison, we adapt existing methods DPS [ 11 ] and DAPS [ 54 ] to make use of the encoder initialization . In both cases, our suggested initialization improves performance.
Figure 14: Noise schedule for incomplete scans. Using cosine annealing for the noise level (rather than constant) and increasing the number of steps from 2000 (2k) to 5000 (5k) is beneficial for incomplete point cloud scans.