Mitigating Memorization in Closed-Form Flow Matching with Bootstrap Aggregating

Diffusion and flow matching are a class of generative models that generate new samples by solving ordinary or stochastic differential equations with a learned score/velocity field. Interestingly, the optimal velocity field admits a closed-form formula that can be computed for finite datasets. Generating samples following the optimal velocity field can only reproduce samples from the training set, i.e., memorize the training set. Neural networks, trained to match the velocity field, introduce inductive bias that can partially mitigate the issue. However, these models can still exhibit memorization, unlike the benign overfitting observed in discriminative tasks. In this paper, we propose a bootstrap aggregating (bagging) method for flow matching to reduce memorization. By conceptually averaging over resampled training subsets, our approach effectively reduces memorization. We derive a closed-form bagging formulation compatible with exact flow matching, enabling efficient implementation. Experiments confirm reduced memorization and better generalization without architectural changes or auxiliary objectives.