Aligning Latent Geometry for Spherical Flow Matching in Image Generation
Summary
This paper proposes aligning latent geometry for spherical flow matching, projecting latents onto a fixed-radius sphere and using spherical linear interpolation to improve image generation quality, consistently improving FID on class-conditional ImageNet.
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Paper page - Aligning Latent Geometry for Spherical Flow Matching in Image Generation
Source: https://huggingface.co/papers/2605.15193
Abstract
Geodesic flow matching improves image generation by projecting latents onto fixed radius spheres and using spherical linear interpolation instead of linear paths, preserving semantic content through angular components.
Latent flow matchingfor image generation usually transportsGaussian noisetovariational autoencoderlatents along linear paths. Both endpoints, however, concentrate in thinspherical shells, and a Euclidean chord leaves those shells even when preprocessing aligns their radii. By decomposing each latent token intoradial 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 ofGaussian noiseas the spherical prior, finetune the decoder with the encoder frozen, and replace linear interpolation withspherical linear interpolation. The resultinggeodesic pathsstay on the sphere at every timestep, and their velocity targets are purely angular by construction. Under matched training, the method consistently improves class-conditional ImageNet-256 FID across differentimage tokenizers, leaves thediffusion architectureunchanged, and requires no auxiliary encoder or representation-alignment objective.
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