This paper clarifies that Diffusion Maps (DMAPs) are not actually a dimensionality reduction tool, but rather a spectral representation that requires specific combinations to form a chart.
March 31, 2026
Original Paper
Diffusion Maps is not Dimensionality Reduction
arXiv · 2603.28037
The Takeaway
It breaks the common assumption that top diffusion coordinates provide an isometric embedding of data manifolds. This finding necessitates a change in how researchers approach manifold learning and latent space visualization.
From the abstract
Diffusion maps (DMAP) are often used as a dimensionality-reduction tool, but more precisely they provide a spectral representation of the intrinsic geometry rather than a complete charting method. To illustrate this distinction, we study a Swiss roll with known isometric coordinates and compare DMAP, Isomap, and UMAP across latent dimensions. For each representation, we fit an oracle affine readout to the ground-truth chart and measure reconstruction error. Isomap most efficiently recovers the l