SpeechIEM: A Label-Free Perceptual Distance for Speech

We present SpeechIEM, a label-free full-reference distance on self- supervised speech latents, and—the point of the paper—the criterion that decides whether such a construction is a distance at all. The construction is the Information-Estimation Metric of Ohayon et al. (2026): a denoiser trained on the data becomes a distance by comparing residuals across noise levels. Its failure mode is silent. The distance becomes a fixed rescaling of the Euclidean distance on the same representation, ordering every pair identically to it, while every training curve improves and every monotonic- ity plot looks healthy. We give the exact condition for that collapse—the denoiser’s action on the difference integrating to a multiple of the identity— and show a scalar action to be sufficient but not necessary, which alone rules out gating on the residual’s direction. Three routes reach the regime in or- dinary practice, one of them an untrained preconditioned denoiser, so a gate is a mandatory step rather than a diagnostic nicety. Which diagnostic to gate on we settle by measurement over 27 denoisers from three grids, scoring each candidate against what it stands in for: the measure-weighted residual cosine rejects two metrics carrying a full advantage, the dispersion of the distance-to-Euclidean ratio rejects none and separates the classes with a factor-of-fifteen empty margin. Admissible, SpeechIEM beats the Euclidean baseline the construction itself contains by +0.058 τb across six distortion families against PESQ, with no quality labels—but the sign of that advantage depends on the reference it is scored against (−0.012 against ESTOI), and on twelve of the thirteen hidden states the trained denoiser adds almost nothing. Hence a reporting standard for this family of metrics: beat the zero-denoiser baseline on the same representation, pair the com- parison, and name the reference quality and the corruption distribution it was measured on.