Aligning Latent Geometry for Spherical Flow Matching in Image Generation

2026-05-14

AI Summary

This work addresses a limitation in conventional latent flow matching, where Euclidean straight-line interpolation between Gaussian noise and VAE latent representations suffers from endpoint concentration on thin spherical shells, causing trajectories to deviate from the true data manifold. The authors observe that semantic information in the latent space is predominantly encoded in directional (angular) components. Leveraging this insight, they project latent representations onto a fixed-radius hypersphere and construct geodesic paths via spherical linear interpolation (slerp). They propose a spherical flow matching method that relies solely on angular velocity, eliminating the need for auxiliary encoders or explicit alignment targets. Notably, this approach enables fine-tuning of only the decoder while keeping the encoder frozen. Evaluated on class-conditional ImageNet-256 generation across multiple image tokenizers, the method consistently improves FID scores and remains compatible with existing diffusion architectures.

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 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 different image tokenizers, leaves the diffusion architecture unchanged, and requires no auxiliary encoder or representation-alignment objective.

Problem

• latent flow matching
• spherical geometry
• image generation
• variational autoencoder
• geodesic paths

Innovation

• spherical flow matching
• latent geometry
• spherical linear interpolation
• angular representation
• generative modeling