用球面插值生成图像，让潜在空间路径更符合数据分布。
Aligning Latent Geometry for Spherical Flow Matching in Image Generation
- 将潜在变量分解为径向与角向分量，发现语义信息主要由方向决定
- 采用球面线性插值，路径始终在球面上，速度目标纯角向
- 无需额外编码器或对齐损失，兼容现有扩散模型架构
图像生成中的潜在流匹配通常沿直线将高斯噪声映射到变分自编码器的潜在表示。然而，两端都集中在细薄的球壳上，即使预处理对齐半径，欧氏弦仍会脱离这些球壳。通过组件交换探测，我们发现解码后的感知和语义内容主要由方向决定，半径贡献较小。因此，将数据潜在表示投影到固定令牌半径上，使用高斯噪声的径向投影作为球面先验，冻结编码器并微调解码器，将线性插值替换为球面线性插值。由此产生的测地线路径在每个时间步均保持在球面上，其速度目标天然为纯角向。在相同训练条件下，该方法在不同图像分词器下持续提升类别条件下的ImageNet-256 FID，保持扩散架构不变，且无需辅助编码器或表示对齐目标。
原文摘要 · Abstract (English)
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.
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