Sensitivity Decomposition for Predictor-Conditioned Diffusion Speech Enhancement

Diffusion-based speech enhancement systems often combine a deterministic predictor with a generative refinement stage, but it is not clear which component determines how the system responds when test conditions change. We study this question in StoRM, where the predictor output both initializes the reverse diffusion process and acts as its mean-reversion target, while the original noisy mixture is supplied separately to the generative stage. We show that the sensitivity of the enhanced output to a change in noise level can be decomposed exactly into contributions associated with these two conditioning routes. This decomposition reveals a structural asymmetry such that perturbations entering through the predictor affect the reverse process from its initial state, whereas perturbations entering only through score conditioning act through the subsequent dynamics. Our measurements show that the diffusion stage does not simply copy the predictor output; it substantially reshapes perturbations introduced through this route. Nevertheless, the predictor-associated contribution remains strongly aligned with the overall response of the enhanced signal. Extending the analysis from local sensitivities to finite changes in noise level leads to the same conclusion: near the training condition, the predictor route determines the direction of the output change, while the direct noisy-mixture conditioning contributes a substantially smaller, largely complementary component. Replacing the predictor-based reference with the noisy mixture causes the system to track the noisy signal instead of enhancing it, providing an independent intervention on the same mechanism. Together, these results identify the conditioning route that anchors the reverse process as the dominant source of robustness behavior in the model studied here. The analysis extends naturally to other differentiable generative samplers with multiple conditioning inputs.