Dataset distillation seeks to synthesize a compact distilled dataset, enabling models trained on it to achieve performance comparable to models trained on the full dataset. Recent methods for large-scale datasets focus on matching global distributional statistics (e.g., mean and variance), but overlook critical instance-level characteristics and intraclass variations, leading to suboptimal generalization. We address this limitation by reformulating dataset distillation as an Optimal Transport (OT) distance minimization problem, enabling fine-grained alignment at both global and instance levels throughout the pipeline. OT offers a geometrically faithful framework for distribution matching. It effectively preserves local modes, intra-class patterns, and fine-grained variations that characterize the geometry of complex, high-dimensional distributions. Our method comprises three components tailored for preserving distributional geometry: (1) OT-guided diffusion sampling, which aligns latent distributions of real and distilled images; (2) label-image-aligned soft relabeling, which adapts label distributions based on the complexity of distilled image distributions; and (3) OT-based logit matching, which aligns the output of student models with soft-label distributions. Extensive experiments across diverse architectures and large-scale datasets demonstrate that our method consistently outperforms state-of-the-art approaches in an efficient manner, achieving at least 4% accuracy improvement under IPC=10 settings for each architecture on ImageNet-1K.