ManifoldDiffusionGeometry

Code for "Manifold Diffusion Geometry: Curvature, Tangent Spaces, and Dimension" https://arxiv.org/abs/2411.04100

This work builds on the programme of "diffusion geometry" introduced in https://arxiv.org/abs/2405.10858 and applies those methods to the special case of manifolds.

This repository contains the following:

1. intro_notebook.ipynb demonstrates all the main methods
2. ManifoldDiffusionGeometry.py defines the main functions

The figures, tests, and auxiliary functions from the paper are in

3. tangents_figs_tests.ipynb
4. dimension_figs_tests.ipynb
5. curvature_figs_tests.ipynb
6. Visualise.py
7. paper_utils.py

The other methods we compare with in the paper are in the 'Other_methods' folder.