Generalization and Memorization in Rectified Flow

Abstract

Generative models based on the Flow Matching objective, particularly Rectified Flow, have emerged as a dominant paradigm for efficient, high-fidelity image synthesis. However, while existing research heavily prioritizes generation quality and architectural scaling, the underlying dynamics of how RF models memorize training data remain largely underexplored. In this paper, we systematically investigate the memorization behaviors of RF through the test statistics of Membership Inference Attacks (MIA). We progressively formulate three test statistics, culminating in a complexity-calibrated metric ($T_\text{mc\_cal}$) that successfully decouples intrinsic image spatial complexity from genuine memorization signals. This calibration yields a significant performance surge -- boosting attack AUC by up to 15\% and the privacy-critical TPR@1\%FPR metric by up to 45\% -- establishing the first non-trivial MIA specifically tailored for RF. Leveraging these refined metrics, we uncover a distinct temporal pattern: under standard uniform temporal training, a model's susceptibility to MIA strictly peaks at the integration midpoint, a phenomenon we justify via the network's forced deviation from linear approximations. Finally, we demonstrate that substituting uniform timestep sampling with a Symmetric Exponential (U-shaped) distribution effectively minimizes exposure to vulnerable intermediate timesteps. Extensive evaluations across three datasets confirm that this temporal regularization suppresses memorization while preserving generative fidelity.

Figures (8)

• Figure 1: MIA performance (AUC and TPR@1%FPR, at left and right respectively) across integration timesteps $t$ on CIFAR-10 and SVHN (top row and bottom row). Our complexity-calibrated statistic ($T_\text{mc\_cal}$) demonstrates a substantial performance surge over the baselines ($T_\text{naive}$ and $T_\text{mc}$).
• Figure 2: Training dynamics (FID and peak AUC) when employing a Symmetric Exponential distribution for timestep sampling. Increasing the concentration parameter $\alpha$ (shown in order of Blue [none], Green, Orange [most]) effectively decelerates and suppresses model memorization while fully preserving generative fidelity.
• Figure 3: Top row: The test statistics $T_\text{mc}$ without calibration. Bottom row: The test statistics $T_\text{mc}$ with calibration. The calibrated version provides more separable points between $\mathcal{D}_\text{train}$ and $\mathcal{D}_\text{val}$
• Figure 4: The gap between $v_\theta$ and $v_\text{linear}$ for $\mathcal{D}_\text{train}$ and $\mathcal{D}_\text{val}$. Solid lines denote the mean, while the shaded areas indicate $\pm$ standard deviation.
• Figure 5: The dynamic with increasing number of Monte Carlo samples on $T_\text{mc}$ and $T_\text{mc\_cal}$

Theorems & Definitions (1)

• proof