Understanding Generalization in Diffusion Distillation via Probability Flow Distance

Diffusion distillation provides an effective approach for learning lightweight and few-steps diffusion models with efficient generation. However, evaluating their 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 ($\mathtt{\text{PFD}}$), a theoretically grounded and computationally efficient metric to measure generalization. Specifically, $\mathtt{\text{PFD}}$ quantifies the distance between distributions by comparing their noise-to-data mappings induced by the probability flow ODE. Using $\mathtt{\text{PFD}}$ under the diffusion distillation setting, we empirically uncover several key generalization behaviors, including: (1) quantitative scaling behavior from memorization to generalization, (2) epoch-wise double descent training dynamics, and (3) bias-variance decomposition. Beyond these insights, our work lays a foundation for generalization studies in diffusion distillation and bridges them with diffusion training.