Summary
Field: Computer Vision (CV) Authors: Tuna Han Salih Meral, Kaan Oktay, Hidir Yesiltepe, Adil Kaan Akan, Pinar Yanardag Published: 2026-05-14 arXiv: 2605.15193
Original Abstract
Latent flow matching for image generation usually transports Gaussian noise to variational autoencoder latents along linear paths. Both endpoints, however, concentrate in thin spherical shells, and a Euclidean chord leaves those shells even when preprocessing aligns their radii. By decomposing each latent token into radial and angular components, we show through component-swap probes that decoded perceptual and semantic content is carried predominantly by direction, with radius contributing much less. We therefore project data latents onto a fixed token radius, use the radial projection of Gaussian noise as the spherical prior, finetune the decoder with the encoder frozen, and replace linear interpolation with spherical linear interpolation. The resulting geodesic paths stay on the sphere ...
Key Points
- Problem: Standard latent flow matching uses linear (Euclidean) interpolation between Gaussian noise and VAE latents, but both distributions lie on thin spherical shells, causing chords to deviate outside the manifold.
- Diagnostic finding: Component-swap probes reveal that the angular (directional) component of latent tokens carries most decoded perceptual and semantic content, while radius contributes comparatively little.
- Method:
- Project data latents onto a fixed token radius.
- Use the radial projection of Gaussian noise as the spherical prior.
- Finetune the decoder with the encoder frozen.
- Replace linear interpolation with spherical linear interpolation (SLERP) so that geodesic paths remain on the sphere.
- Contribution: Aligns the geometry of the latent space with its true spherical structure, improving geometric consistency for image generation.