MATH · IN · MODELS

DDPM (Denoising Diffusion Probabilistic Models, HuggingFace Diffusers checkpoints)

Ho, Jain & Abbeel / HuggingFace

Structures found in this family (2)

Linear Direction, Curvature profile of the representation manifold

By model (10)

DDPM (CIFAR-10, unconditional)
Curvature profile of the representation manifold, Linear Direction
DDPM+P2-weighting (AFHQ 256x256)
Linear Direction
DDPM (CelebA-HQ 256x256, HuggingFace Diffusers)
Linear Direction
DDPM+P2-weighting (FFHQ 256x256)
Linear Direction
DDPM+P2-weighting (Flowers 256x256)
Linear Direction
DDPM (ImageNet 256x256)
Linear Direction
DDPM (LSUN-Bedroom 256x256, HuggingFace Diffusers)
Linear Direction
DDPM (LSUN-Cat 256x256)
Linear Direction
DDPM (LSUN-Church 256x256, HuggingFace Diffusers)
Linear Direction
DDPM (LSUN-Horse 256x256)
Linear Direction

Observations (4)

A pullback Riemannian metric yields diffusion tangent-space directions
Diffusion h-space directions arise from PCA, Jacobian SVD, and diff-of-means
A real DDPM's Critical Boundary Detector correlates with LPIPS and localizes classifier-guidance-worthy timesteps
A single RFM/AGOP direction per concept steers diffusion at a fraction of guidance cost

Papers

Understanding the Latent Space of Diffusion Models through the Lens of Riemannian Geometry (2023), Discovering Interpretable Directions in the Semantic Latent Space of Diffusion Models (2023), The Geometry of Phase Transitions in Generative Dynamics via Projection Caustics (2026), General and Efficient Steering of Diffusion Models (2026)