  The diffusion probabilistic generative models are widely used to generate
high-quality data. Though they can synthetic data that does not exist in the
training set, the rationale behind such generalization is still unexplored. In
this paper, we formally define the generalization of the generative model,
which is measured by the mutual information between the generated data and the
training set. The definition originates from the intuition that the model which
generates data with less correlation to the training set exhibits better
generalization ability. Meanwhile, we show that for the empirical optimal
diffusion model, the data generated by a deterministic sampler are all highly
related to the training set, thus poor generalization. This result contradicts
the observation of the trained diffusion model's (approximating empirical
optima) extrapolation ability (generating unseen data). To understand this
contradiction, we empirically verify the difference between the sufficiently
trained diffusion model and the empirical optima. We found, though obtained
through sufficient training, there still exists a slight difference between
them, which is critical to making the diffusion model generalizable. Moreover,
we propose another training objective whose empirical optimal solution has no
potential generalization problem. We empirically show that the proposed
training objective returns a similar model to the original one, which further
verifies the generalization ability of the trained diffusion model.
