  How do score-based generative models (SBMs) learn the data distribution
supported on a low-dimensional manifold? We investigate the score model of a
trained SBM through its linear approximations and subspaces spanned by local
feature vectors. During diffusion as the noise decreases, the local
dimensionality increases and becomes more varied between different sample
sequences. Importantly, we find that the learned vector field mixes samples by
a non-conservative field within the manifold, although it denoises with normal
projections as if there is an energy function in off-manifold directions. At
each noise level, the subspace spanned by the local features overlap with an
effective density function. These observations suggest that SBMs can flexibly
mix samples with the learned score field while carefully maintaining a
manifold-like structure of the data distribution.
