Visualizing probability paths in diffusion: straight lines vs elliptical arcs

alec_helbling · x · 2026-10-23

A technical visual explainer: probability paths describe how a distribution evolves from source to target. The Linear Path connects each paired sample with a straight line, while the Variance-Preserving Path uses cosine–sine interpolation to trace a curved, elliptical arc. The attached figure contrasts the geometry of the two paths.

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