Generalization and Memorization in Rectified Flow

TL;DR

This paper investigates how Rectified Flow models memorize training data, introduces new metrics to measure memorization, and proposes a temporal regularization method to reduce memorization without sacrificing image quality.

Contribution

It develops a complexity-calibrated metric for memorization detection, uncovers temporal patterns in memorization susceptibility, and introduces a novel sampling strategy to mitigate memorization in RF models.

Findings

Memorization peaks at the training midpoint under standard methods.

The new metric $T_{mc extunderscore cal}$ improves attack detection performance.

Temporal regularization reduces memorization while maintaining image quality.

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.