Instruction-driven editing of 3D human motion requires precise spatiotemporal localization, rich semantic grounding, and strict preservation of unmodified content. Existing methods either resort to training-free adaptation of generative models or rely solely on triplet supervision; however, adaptation often yields suboptimal control, and manually curated triplet datasets remain severely limited in scale and semantic diversity. To overcome this bottleneck, we ground motion editing directly within text-to-motion generation across data, architecture, and inference. At the data level, we develop a closed-loop synthesis-and-verification pipeline that produces Omni-MoEdit, a large-scale dataset spanning body-part, amplitude, temporal, action, and style edits. At the architectural level, we introduce UniMoFlow, a unified latent flow-matching model that shares broad semantic and kinematic knowledge between generation and editing. At the inference level, SAFE (Source-Anchored Flow Editing) complements UniMoFlow with controllable, source-anchored refinement. Furthermore, we augment standard evaluations with semantics-aware metrics to account for valid edits that inherently deviate from a single ground-truth reference. Extensive experiments demonstrate improved target-text alignment, edit effectiveness, and cycle consistency, while maintaining competitive source fidelity and text-to-motion generation quality.

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