score-matching

This paper identifies a collapse-and-refine mechanism in diffusion models under the manifold hypothesis, proposing Score-induced Latent Diffusion (SiLD) that provably avoids the curse of dimensionality. Experiments show SiLD matches or outperforms VAE-based latent diffusion models.

This paper provides the first non-asymptotic sample complexity bounds for learning exponential families of polynomials with score matching, showing polynomial dependence on model dimension.