Title: Localized Analysis of Continuous Normalizing Flows for Out-of-Distribution Identification

Abstract

This study tackles the challenge of detecting out-of-distribution (OOD) observations that reside within a subspace of high-dimensional data. We introduce a Lagrangian sub-flow (LSF) framework leveraging continuous normalizing flows (CNFs), which functions by estimating the density of pertinent components within the representation while treating the remaining elements as contextual information.

Experiments conducted on speech synthesis models reveal that CNFs, much like other deep generative models (DGMs), fall prey to the "likelihood paradox." In this scenario, OOD samples are incorrectly assigned high likelihood values. We attribute this issue to the inductive biases inherent in DGMs, which tend to emphasize low-level structural nuances at the expense of high-level semantic consistency.

To address this limitation, we develop several geometric diagnostic signals derived from the velocity field along the sub-flow trajectory. Utilizing these signals, we construct metrics tailored for the difficult task of zero-shot, phoneme-level mispronunciation detection. Our results demonstrate that these new metrics outperform traditional likelihood-based approaches when evaluated on a real-world mispronunciation detection benchmark.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC