Open-vocabulary 3D Gaussian segmentation typically binds semantic features to the per-Gaussian state via per-scene gradient training (1-4 h) or the more recent closed-form distillation. Both commit each primitive to a single feature; therefore, boundary Gaussians spanning multiple 2D instances are forced into a hard decision that degrades retrieval accuracy and yields unstable mask boundaries at render time. We present DIGS, a training-free framework with two stages, class-agnostic mapping and multi-modal encoding, that decouples instance discovery from linguistic naming. At the Gaussian level, our distribution-informed representation maintains an explicit top-$M$ label distribution per primitive, updated by a tempered Dirichlet rule; preservation of multi-peaked label distributions at boundary primitives allows a late-argmax renderer to recover clean instance boundaries. A bidirectional state machine aggregates these distributions into a persistent class-agnostic instance ontology. The instance-level encoding stage then fuses the CLIP visual embedding of each instance's isolated 3D footprint with the CLIP-text embedding of an LLM-generated attribute description, disambiguating visually similar instances. On a single A100, DIGS completes mapping and instance encoding on LERF-OVS in 1.0-3.2 min per scene, depending on whether LLM fusion is enabled, and serves native 3D queries in 5.4 ms. It reaches 71.95% mean mIoU on LERF-OVS, outperforming both the training-free SFS and training-based LaGa baselines. DIGS also achieves the highest mean mIoU on LERF-Mask and 3D-OVS and surpasses Gaga and ObjectGS on Replica under their respective evaluation protocols. Code is available at https://github.com/ZephyrZos/DIGS.

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