mlsanityData to 14 Oct 2026

On the Structural Failure of Chamfer Distance in 3D Shape Optimization

arXiv 2603.09925 ↗First posted 10 Mar 2026cs.CV cs.GRcited by 0

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Abstract (arXiv)

Chamfer distance is the standard training loss for point cloud reconstruction, completion, and generation, yet directly optimizing it can produce worse Chamfer values than not optimizing it at all. We show that this paradoxical failure is gradient-structural. The per-point Chamfer gradient creates a many-to-one collapse that is the unique attractor of the forward term and cannot be resolved by any local regularizer, including repulsion, smoothness, and density-aware re-weighting. We derive a necessary condition for collapse suppression: coupling must propagate beyond local neighborhoods. In a controlled 2D setting, shared-basis deformation suppresses collapse by providing global coupling; in 3D shape morphing, a differentiable MPM prior instantiates the same principle, consistently reducing the Chamfer gap across 20 directed pairs with a 2.5× improvement on the topologically complex dragon. The presence or absence of non-local coupling determines whether Chamfer optimization succeeds or collapses. This provides a practical design criterion for any pipeline that optimizes point-level distance metrics.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 38 of its 59 references that are in the map. First posted on arXiv 10 Mar 2026.

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References · 38

  1. 20233D Gaussian Splatting for Real-Time Radiance Field Renderingcited by 6,226
  2. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,248
  3. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,401
  4. 2018Neural Ordinary Differential Equationscited by 3,779
  5. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,689
  6. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  7. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,041
  8. 2021NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstructioncited by 1,712
  9. 20234D Gaussian Splatting for Real-Time Dynamic Scene Renderingcited by 1,157
  10. 2018Learning Implicit Fields for Generative Shape Modelingcited by 1,060
  11. 2016A Point Set Generation Network for 3D Object Reconstruction from a Single Imagecited by 979
  12. 2023Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstructioncited by 759
26 more
  1. 2023Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesiscited by 737
  2. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 735
  3. 2020Implicit Geometric Regularization for Learning Shapescited by 710
  4. 2019Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervisioncited by 700
  5. 2018Pixel2Mesh: Generating 3D Mesh Models from Single RGB Imagescited by 651
  6. 2018AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generationcited by 539
  7. 2019PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flowscited by 488
  8. 2019SAL: Sign Agnostic Learning of Shapes from Raw Datacited by 390
  9. 2019DiffTaichi: Differentiable Programming for Physical Simulationcited by 258
  10. 2018PU-Net: Point Cloud Upsampling Networkcited by 209
  11. 2020GRNet: Gridding Residual Network for Dense Point Cloud Completioncited by 174
  12. 2020Cascaded Refinement Network for Point Cloud Completioncited by 112
  13. 2021Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completioncited by 112
  14. 2019Pixel2Mesh++: Multi-View 3D Mesh Generation via Deformationcited by 103
  15. 2021PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physicscited by 103
  16. 2021gradSim: Differentiable simulation for system identification and visuomotor controlcited by 100
  17. 2018ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Roboticscited by 98
  18. 2018EC-Net: an Edge-aware Point set Consolidation Networkcited by 84
  19. 2021NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Gocited by 81
  20. 2020Distributional Sliced-Wasserstein and Applications to Generative Modelingcited by 69
  21. 2020Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flowscited by 61
  22. 2020LIMP: Learning Latent Shape Representations with Metric Preservation Priorscited by 55
  23. 2020DPDist : Comparing Point Clouds Using Deep Point Cloud Distancecited by 22
  24. 2018Divergence-Free Shape Interpolation and Correspondencecited by 6
  25. 2023Learnable Chamfer Distance for Point Cloud Reconstructioncited by 4
  26. 2024A Differentiable Material Point Method Framework for Shape Morphingcited by 1

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