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$\times$ 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.

翻译：Chamfer 距离是点云重建、补全与生成任务中的标准训练损失函数，然而直接优化该损失可能产生比完全不优化更差的 Chamfer 值。我们证明，这种看似矛盾的失效本质上是梯度结构性的。逐点 Chamfer 梯度会产生多对一的坍缩现象，该现象是前向项的唯一定点吸引子，且无法通过任何局部正则化方法（包括斥力项、平滑约束和密度感知重加权）予以解决。我们推导出抑制坍缩的必要条件：耦合作用必须传播至局部邻域之外。在受控的二维场景中，共享基变形通过提供全局耦合有效抑制了坍缩；在三维形状变形任务中，可微分 MPM 先验实现了相同原理，在 20 组定向形状对中持续缩小了 Chamfer 差距，并在拓扑结构复杂的龙模型上实现了 2.5 倍的性能提升。非局部耦合的存在与否决定了 Chamfer 优化最终会成功还是发生坍缩。这一发现为所有优化点级距离度量的流程提供了实用的设计准则。