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This paper investigates how Rectified Flows, a class of generative models, retain information from their training data, focusing on the interpolation path defined by $X_\lambda = (1-\lambda)X_0 + \lambda X_1$. The authors reveal a bell-shaped curve in the reconstruction gap between training and test data, which accumulates during training despite stable validation metrics, and derive the peak location under Gaussian assumptions. Through empirical validation on audio and images, they demonstrate the universality of this structure and utilize it to conduct a Membership Inference Attack, effectively distinguishing training set members from non-members.
A hidden bell-shaped curve in generative model training reveals exploitable membership signals that could threaten privacy.
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 $X_\lambda = (1-\lambda)X_0 + \lambda X_1$ 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 $\lambda$, 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 $\lambda$-resolved structure to perform a Membership Inference Attack, distinguishing members of the training set from non-members.
