Interactive 3D segmentation of a reconstructed scene should not require a representation-specific optimization loop. We observe that the recipe for lifting 2D foundation-model masks into 3D, namely prompting a few views, refining the resulting masks with rendered depth, and fusing the multi-view evidence into a voxel grid, is shared across scene representations. What remains representation-specific is only the depth signal returned by the renderer and the occupancy prior that gates fusion. We present **DivAS** (Depth-interactive Voxel Aggregation Segmentation), an optimization-free, training-free framework that realizes this recipe as a single interaction-and-fusion skeleton with lightweight, representation-specific adapters, instantiated on both Gaussian Splatting (GS) and NeRF backbones. On standard forward-facing and unbounded benchmarks, the GS instantiation attains segmentation quality competitive with state-of-the-art optimization-based methods, and the best on LLFF, while being the only one to reach this quality within the consumer-hardware memory envelope at standard resolution. Both instantiations run end-to-end around $2$x faster than feature-field baselines, with a per-update fusion-kernel cost below $70$ ms. Because segmentation evidence is gathered from a small, bounded set of anchor views, user effort and computation remain independent of the training-set size. The same skeleton applied to a NeRF backbone matches or exceeds the performance of optimization-based NeRF baselines, confirming that the recipe transfers across fundamentally different 3D representations.

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