# The Spacetime of Diffusion Models: An Information Geometry Perspective

### TL;DR

We redefine the latent space of diffusion models as a spacetime continuum $(\mathbf{x}_t,t)$. Using ideas from information geometry, we impose a geometric structure that captures how the denoising distribution changes as we move through latent spacetime. Surprisingly, we can compute shortest paths efficiently—even in high dimensions.

| ![](curve_with_density.gif) | 
|:--:| 
| **Fig1: Spacetime geodesic is the shortest path between denoising distributions.** Each point on the spacetime curve $(\mathbf{x}_t,t)$ (right) corresponds to a denoising distribution $p(\mathbf{x}_0 \mid \mathbf{x}_t)$ (left).|
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### Code structure
Each directory contains instructions on how to set up the necessary environment, and how to run code to reproduce results from the paper.

#### Toy experiments

This directory contains experiments on the toy experiments with 1D Gaussian mixture. These include code necessary to recreate Fig1 and Fig3 (left).

#### Image experiments

This directory contains experiments on image data using the EDM2 model. These are discussed in Section 6.2.

#### Molecular experiments

This directory contains experiments on transition path sampling for molecular data, as discussed in Sections 6.3 and 6.4 in the paper.
