Coherence-Preserving Distribution Matching for 3D Point Cloud Dataset Distillation

Dataset distillation compresses a large training set into a compact synthetic set while preserving its training utility. For 3D point clouds, distribution matching must additionally account for arbitrary point indexing. Existing Semantically Aligned Distribution Matching (SADM) addresses this issue by independently sorting pointwise feature responses within each channel. However, such channel-wise sorting discards the cross-channel associations among responses originating from the same point, introducing an unnecessary invariance to independent channel permutations. We propose Coherence-Preserving Distribution Matching (CPDM), which complements channel-wise matching with a shared point ordering derived from aggregated normalized feature responses. Applying this shared ordering to complete pointwise feature vectors preserves their cross-channel coherence while remaining invariant to point re-indexing. CPDM further employs trained expert checkpoints for feature extraction and auxiliary classification supervision. Theoretically, we show that, under distinct point scores, the full shared-order representation is invariant to shared point permutations and identifiable up to such permutations, avoiding the additional ambiguity induced by independent channel-wise sorting. Experiments on five 3D classification benchmarks demonstrate consistent improvements across a wide range of compression budgets. In the non-parameterized setting, CPDM achieves the highest mean accuracy among the compared methods in 12 of 15 dataset–budget configurations, while its parameterized variant outperforms 3DDP in 14 of 15 configurations. Cross-architecture evaluations and ablation studies further support the transferability and effectiveness of coherence-preserving matching.