Blind source separation has two classical routes to identifiability. One exploits non-Gaussianity — if sources have non-Gaussian distributions, higher-order statistics can distinguish them. The other exploits observation diversity — temporal, spatial, or multi-channel structure in the observations, using only second-order statistics. These routes are taught as fundamentally different methods for fundamentally different reasons.

They are the same mechanism.

Both work by stabilizer shrinkage: reducing the continuous symmetry group of ambiguities in the mixing model to a finite residual group. Before any constraints, the mixing matrix can be rotated by any orthogonal transformation and the observations look the same — continuous ambiguity. Non-Gaussianity constrains which rotations preserve the source statistics. Observation diversity constrains which rotations preserve the observation structure. Both shrink the same symmetry group through different constraints.

The unification is not metaphorical. The paper introduces a Jacobian-based sensitivity probe that measures local identifiability in finite-sample regimes, and shows that increasing non-Gaussianity and increasing observation diversity suppress the same residual symmetry. There is a structural trade-off: you can substitute one for the other. More non-Gaussian sources need less diverse observations. More diverse observations tolerate more Gaussian sources.

This matters because it reframes identifiability as a geometric problem — how much of the ambiguity group survives after constraints — rather than a statistical one. The question is not “do I have enough data?” but “have my constraints killed enough symmetry?” The same residual ambiguity can be attacked from either direction, because both directions target the same group.

Two methods. One mechanism. The difference was in the constraints applied, not in what the constraints acted on.