Fisher-Rao spacetime geodesics

Defines a Fisher-Rao information metric directly on the family of a diffusion model's own denoising distributions {p(x0|xt,t)}, indexed by noisy state and time jointly (the 'spacetime' (x_t,t)), and computes geodesics under this metric via a closed-form, simulation-free curve-energy estimator that exploits the family's exponential form -- distinct from pulling back an ambient Euclidean or activation-space metric through the model's Jacobian, which the technique's own authors prove collapses to a trivial straight-line metric whenever latent and data space share the same dimension.