manifold-hypothesis

This paper studies how β-VAEs act as effective theories where the KL weight acts as a spectral cutoff, and analyzes how nonlinear interactions and network depth affect the tolerance-dependent effective dimension of representations.

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.