Quantifying feature importance with valid statistical uncertainty is central to interpretable machine learning, yet classical model-agnostic methods often fail under feature correlation, producing unreliable attributions and compromising statistical inference. Existing approaches—such as Shapley values and leave-one-covariate-out—are vulnerable to correlation distortion, limiting their robustness across diverse tasks. We introduce Disentangled Feature Importance (DFI), a model-agnostic framework that resolves these limitations by combining principled statistical inference with computational flexibility. DFI leverages optimal transport to learn flexible disentanglement maps and provide an interpretable pathway for understanding how importance is attributed through the data’s correlation structure. The framework generalizes to flow matching and differentiable loss functions, enabling statistically valid importance assessment for black-box predictors in both regression and classification. We establish statistical inference theory, which enables valid confidence intervals and hypothesis testing with Type I error control. Empirical results on synthetic and biomedical datasets show that DFI delivers substantially higher statistical power than removal-based and conditional permutation methods, while maintaining robust, interpretable attributions under severe feature interdependence.