Generalization and Memorization in Rectified Flow

Generative models based on the Flow Matching objective,particularly Rectified Flow, have emerged as a dominant paradigm forefficient, high-fidelity image synthesis. However, while existing researchheavily prioritizes generation quality and architectural scaling, the un-derlying dynamics of how RF models memorize training data remainlargely underexplored. In this paper, we systematically investigate thememorization behaviors of RF through the test statistics of MembershipInference Attacks (MIA). We progressively formulate three test statistics,culminating in a complexity-calibrated metric (Tmc_cal ) that successfullydecouples intrinsic image spatial complexity from genuine memorizationsignals. This calibration yields a significant performance surge—boostingattack AUC by up to 15% and the privacy-critical TPR@1%FPR metricby up to 45%—establishing the first non-trivial MIA specifically tailoredfor RF. Leveraging these refined metrics, we uncover a distinct temporalpattern: under standard uniform temporal training, a model’s suscepti-bility to MIA strictly peaks at the integration midpoint, a phenomenonwe justify via the network’s forced deviation from linear approximations.Finally, we demonstrate that substituting uniform timestep samplingwith a Symmetric Exponential (U-shaped) distribution effectively min-imizes exposure to vulnerable intermediate timesteps. Extensive evalu-ations across three datasets confirm that this temporal regularizationsuppresses memorization while preserving generative fidelity.