Diffusion models have emerged as a powerful class of generative models, capable of producing high-quality samples that generalize beyond the training data. However, evaluating this generalization remains challenging: theoretical metrics are often impractical for high-dimensional data, while no practical metrics rigorously measure generalization. In this work, we bridge this gap by introducing probability flow distance (PFD), a theoretically grounded and computationally efficient metric to measure distributional generalization. Specifically, PFD quantifies the distance between distributions by comparing their noise-to-data mappings induced by the probability flow ODE. Moreover, by using PFD under a teacher-student evaluation protocol, we empirically uncover several key generalization behaviors in diffusion models, including: (1) scaling behavior from memorization to generalization, (2) early learning and double descent training dynamics, and (3) bias-variance decomposition. Beyond these insights, our work lays a foundation for future empirical and theoretical studies on generalization in diffusion models.
Zhang et al. (Mon,) studied this question.
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