Fisher-Rao spacetime metric yields diffusion-model geodesics (DiffED)
measured in 1 paper- Karczewski et al. build a Fisher-Rao metric on the exponential family of a diffusion model's denoising distributions indexed by spacetime (x_t, t), proving the fixed-time version collapses to zero and the Jacobian-pullback version collapses to Euclidean interpolation. [karczewski-etal-2026-spacetime-of-diffusion-models] - Spacetime geodesics define a Diffusion Edit Distance (DiffED), computed simulation-free from one Jacobian-vector product per path point. [karczewski-etal-2026-spacetime-of-diffusion-models] - On EDM2 ImageNet-512 (200 image pairs), DiffED correlates only ~-7% with LPIPS but ~53% with SSIM (correlation type and p-values not reported). [karczewski-etal-2026-spacetime-of-diffusion-models] - On a custom Alanine-Dipeptide diffusion model, geodesic transition paths reach mean max energy barrier 37.36+/-0.60 (numerical lower bound 36.42), beating MCMC (42.54+/-7.42; 58.11+/-18.51) and Doob's Lagrangian (66.24+/-1.01) at far fewer energy evaluations. [karczewski-etal-2026-spacetime-of-diffusion-models]