# Local Diagnostics of Continuous Normalizing Flow for Out-of-Distribution Detection

arXiv: https://arxiv.org/abs/2606.00684 · HTML: https://mlsanity.com/paper/2606.00684/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (2022)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Voicebox: Text-Guided Multilingual Universal Speech Generation at Scale](https://mlsanity.com/paper/2306.15687/) (2023)
- [F5-TTS: A Fairytaler that Fakes Fluent and Faithful Speech with Flow Matching](https://mlsanity.com/paper/2410.06885/) (2024)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Input complexity and out-of-distribution detection with likelihood-based generative models](https://mlsanity.com/paper/1909.11480/) (2019)
- [E2 TTS: Embarrassingly Easy Fully Non-Autoregressive Zero-Shot TTS](https://mlsanity.com/paper/2406.18009/) (2024)
- [Likelihood Regret: An Out-of-Distribution Detection Score For Variational Auto-encoder](https://mlsanity.com/paper/2003.02977/) (2020)
- [Density of States Estimation for Out-of-Distribution Detection](https://mlsanity.com/paper/2006.09273/) (2020)
- [DiffGuard: Semantic Mismatch-Guided Out-of-Distribution Detection using Pre-trained Diffusion Models](https://mlsanity.com/paper/2308.07687/) (2023)
- [A Geometric Explanation of the Likelihood OOD Detection Paradox](https://mlsanity.com/paper/2403.18910/) (2024)
- [Segmentation-free Goodness of Pronunciation](https://mlsanity.com/paper/2507.16838/) (2025)

## Abstract (arXiv)

We address the problem of out-of-distribution (OOD) detection for target observations embedded in a subspace of the high dimensional data space. Using continuous normalizing flows (CNFs), we propose a Lagrangian sub-flow (LSF) framework designed to isolate and estimate the density for the relevant components in the representation and using the remaining components as context. Through experimentation with models for speech synthesis, we show that CNFs, similarly to other deep generative models (DGMs), are susceptible to the "likelihood paradox", where high likelihood is erroneously assigned to OOD samples. This is attributed to the inductive bias of DGMs that prioritize low-level structural details over high-level semantic coherence. To mitigate this phenomenon, we propose a number of geometric diagnostic signals based on the velocity field over the sub-flow trajectory. Based on these signals, we design metrics for the challenging task of zero-shot phoneme-level mispronunciation detection. Finally, we demonstrate the superiority of these metrics compared to likelihood-based methods on a real-world mispronunciation detection benchmark.