Keeping noise-to-image paths on spherical surfaces

Flow matching models typically transport Gaussian noise to image latents along straight lines, but both endpoints concentrate on thin spherical shells—causing Euclidean paths to leave these shells and waste capacity. This work decomposes latent tokens into radial and angular components, finding that direction carries perceptual and semantic content while radius contributes minimally. The method projects data onto fixed token radius, uses spherical linear interpolation instead of Euclidean, and finetunes the decoder. Geodesic paths remain on the sphere throughout. Results show consistent FID improvements on class-conditional ImageNet-256 across multiple tokenizers, requires no new architectural components or alignment objectives, and code is released.