Where Rectified Flows Leak: Characterising Membership Signals Along the Interpolation Path

2026-06-05

AI Summary

This work investigates whether Rectified Flows implicitly leak private information from their training data. By analyzing the interpolation paths they rely on, defined as $X_\lambda = (1-\lambda)X_0 + \lambda X_1$, the study reveals for the first time that reconstruction error exhibits a bell-shaped distribution along $\lambda$. Under Gaussian assumptions, the authors derive a closed-form expression for the location of this peak. Leveraging this $\lambda$-resolved signal, they propose a novel membership inference attack. Experiments on image and audio datasets demonstrate the universality of the bell-shaped error structure and the accuracy of the predicted peak location. The resulting attack significantly outperforms existing baselines, offering a new perspective on privacy risks in generative modeling.

Abstract

Understanding what generative models retain from training data 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 study this regime for Rectified Flows, which are increasingly used in deployed generative systems. We analyse the interpolation path $X_λ= (1-λ)X_0 + λX_1$ that defines the Rectified Flow training. We show that a gap exists between the reconstruction of train and test data that follows a bell-shaped curve over $λ$, wich 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.

Problem

• Rectified Flows
• Membership Inference
• Training Data Leakage
• Interpolation Path
• Generative Models

Innovation

• Rectified Flows
• Membership Inference Attack
• Interpolation Path
• Data Leakage
• Reconstruction Gap