# Where Flow Matching Leaks: Characterising Membership Signals Along the Interpolation Path

arXiv: https://arxiv.org/abs/2606.07271 · HTML: https://mlsanity.com/paper/2606.07271/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 26 of 26)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Voicebox: Text-Guided Multilingual Universal Speech Generation at Scale](https://mlsanity.com/paper/2306.15687/) (2023)
- [Memorization Without Overfitting: Analyzing the Training Dynamics of Large Language Models](https://mlsanity.com/paper/2205.10770/) (2022)
- [Enabling Factorized Piano Music Modeling and Generation with the MAESTRO Dataset](https://mlsanity.com/paper/1810.12247/) (2018)
- [FMA: A Dataset For Music Analysis](https://mlsanity.com/paper/1612.01840/) (2016)
- [Stable Audio Open](https://mlsanity.com/paper/2407.14358/) (2024)
- [Training behavior of deep neural network in frequency domain](https://mlsanity.com/paper/1807.01251/) (2018)
- [Counterfactual Memorization in Neural Language Models](https://mlsanity.com/paper/2112.12938/) (2021)
- [Are Diffusion Models Vulnerable to Membership Inference Attacks?](https://mlsanity.com/paper/2302.01316/) (2023)
- [On Memorization in Diffusion Models](https://mlsanity.com/paper/2310.02664/) (2023)
- [Membership Inference Attacks against Diffusion Models](https://mlsanity.com/paper/2302.03262/) (2023)
- [Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training](https://mlsanity.com/paper/2505.17638/) (2025)
- [An Efficient Membership Inference Attack for the Diffusion Model by Proximal Initialization](https://mlsanity.com/paper/2305.18355/) (2023)
- [On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity](https://mlsanity.com/paper/2506.03719/) (2025)
- [Music2Latent: Consistency Autoencoders for Latent Audio Compression](https://mlsanity.com/paper/2408.06500/) (2024)

## Abstract (arXiv)

Understanding memorization in generative models remains challenging, with implications for copyright and privacy. Beyond verbatim reproduction, models can encode subtler traces of their training data that never surface in their outputs yet remain exploitable. We refer to these measurable asymmetries as the membership signal, and we study this regime for Flow Matching, which are increasingly used in deployed generative systems. We analyze the linear interpolation path Xλ = (1-λ)X0 + λ X1 that defines standard Flow Matching training. We show that a gap exists between the reconstruction of train and test data that follows a bell-shaped curve over λ, which accumulates during training, while the validation metrics remain stable. The signal has a maximum whose location we derive in closed form under Gaussian assumptions. We validate these predictions on both audio and images and show that the bell-shaped structure is universal, while the peak prediction holds when our assumptions are satisfied. As a proof of concept, we exploit this specific λ-resolved structure to perform a Membership Inference Attack, distinguishing members of the training set from non-members.