ManifoldGD: Training-Free Hierarchical Manifold Guidance for Diffusion-Based Dataset Distillation

Abstract: In recent times, large datasets hinder efficient model training while also containing redundant concepts. Dataset distillation aims to synthesize compact datasets that preserve the knowledge of large-scale training sets while drastically reducing storage and computation. Recent advances in diffusion models have enabled training-free distillation by leveraging pre-trained generative priors; however, existing guidance strategies remain limited. Current score-based methods either perform unguided denoising or rely on simple mode-based guidance toward instance prototype centroids (IPC centroids), which often are rudimentary and suboptimal. We propose Manifold-Guided Distillation (ManifoldGD), a training-free diffusion-based framework that integrates manifold consistent guidance at every denoising timestep. Our method employs IPCs computed via a hierarchical, divisive clustering of VAE latent features, yielding a multi-scale coreset of IPCs that captures both coarse semantic modes and fine intra-class variability. Using a local neighborhood of the extracted IPC centroids, we create the latent manifold for each diffusion denoising timestep. At each denoising step, we project the mode-alignment vector onto the local tangent space of the estimated latent manifold, thus constraining the generation trajectory to remain manifold-faithful while preserving semantic consistency. This formulation improves representativeness, diversity, and image fidelity without requiring any model retraining. Empirical results demonstrate consistent gains over existing training-free and training-based baselines in terms of FID, l2 distance among real and synthetic dataset embeddings, and classification accuracy, establishing ManifoldGD as the first geometry-aware training-free data distillation framework.