Towards Principled Dataset Distillation: A Spectral Distribution Perspective

Dataset distillation compresses large-scale datasets into compact synthetic sets while preserving their training utility, enabling efficient 3D point cloud training. Current point cloud dataset distillation methods only tackle geometric and representation challenges while ignoring the distributional imbalance prevalent in point cloud datasets where both training and test splits follow long-tailed class distributions. To our knowledge, we present the first study on long-tailed point cloud dataset distillation. Rather than focusing primarily on geometric and representation properties or simply constructing a class-balanced synthetic set, our framework explicitly accounts for long-tailed class distributions via two core modules. First, we design Adaptive Synthetic Budgeting to allocate class-wise synthetic budgets according to class quantity and the expected benefit of additional synthetic samples. Given the allocated budgets, we further design 3D Long-Tailed Distribution Matching to optimize synthetic point clouds through Global-Local Feature Alignment and Prior-Aware Supervision. The former preserves both global class distributions and diverse intra-class structures, while the latter provides class-dependent expert supervision to keep tail-class samples recognizable while maintaining diverse head-class patterns. Extensive experiments demonstrate the effectiveness of our method, lifting classification accuracy by 7.0 points on ShapeNet55 against state-of-the-art methods.

Dataset Distillation (DD) synthesizes a compact synthetic dataset that preserves the training utility of a full dataset. However, its standard formulation assumes that test data follow the same distribution as training data, an assumption that rarely holds in practice. A straightforward extension-applying post-hoc Domain Generalization (DG) techniques to distilled data-is ill-suited because existing DG methods rely on the natural diversity of real datasets, which compact synthetic sets inherently lack, while also incurring substantial augmentation overhead that conflicts with the efficiency objective of dataset distillation. To address this limitation, we introduce Domain Generalizable Dataset Distillation (DGDD), a new problem setting that explicitly targets out-of-distribution (OOD) generalization of distilled datasets. We study this problem through a widely adopted DD baseline of Distribution Matching (DM). We attribute the OOD vulnerability of DM to the entanglement of class-discriminative and domain-specific information within the compressed synthetic set, and propose Spectral Gradient Surgery (SGS) to disentangle the two. The key insight of SGS is that cross-domain agreement among domain-wise gradients in the spectral domain reveals which gradient components are shared across source domains-and are therefore class-discriminative-and which are domain-specific. Based on this observation, SGS augments the standard DM update with two complementary gradients: one that reinforces cross-domain shared components and another that explicitly promotes diversity within the distilled dataset. Extensive experiments on diverse-scale benchmarks demonstrate that SGS substantially improves OOD generalization while remaining plug-and-play compatible with existing DM methods.

Dataset Distillation aims to synthesize compact datasets that can approximate the training efficacy of large-scale real datasets, offering an efficient solution to the increasing computational demands of modern deep learning. Recently, diffusion-based dataset distillation methods have shown great promise by leveraging the strong generative capacity of diffusion models to produce diverse and structurally consistent samples. However, a fundamental goal misalignment persists: diffusion models are optimized for generative likelihood rather than discriminative utility, resulting in over-concentration in high-density regions and inadequate coverage of boundary samples crucial for classification. To address this issue, we propose two complementary strategies. Inversion-Matching (IM) introduces an inversion-guided fine-tuning process that aligns denoising trajectories with their inversion counterparts, broadening distributional coverage and enhancing diversity. Selective Subgroup Sampling(S^3) is a training-free sampling mechanism that improves inter-class separability by selecting synthetic subsets that are both representative and distinctive. Extensive experiments demonstrate that our approach significantly enhances the discriminative quality and generalization of distilled datasets, achieving state-of-the-art performance among diffusion-based methods.