Score-based generative models learn manifold-like structures with constrained mixing

Understand

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.