Score-Based Generative Models Detect Manifolds. (arXiv:2206.01018v2 [stat.ML] UPDATED)

Score-based generative models (SGMs) need to approximate the scores $\nabla
\log p_t$ of the intermediate distributions as well as the final distribution
$p_T$ of the forward process. The theoretical underpinnings of the effects of
these approximations are still lacking. We find precise conditions under which
SGMs are able to produce samples from an underlying (low-dimensional) data
manifold $\mathcal{M}$. This assures us that SGMs are able to generate the
"right kind of samples". For example, taking $\mathcal{M}$ to be the subset …

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