SphereFlow: Missing Modality Imputation via Geometric Transport on Hypersphere

Huihan Wang, Juncheng Wang, Yuxiang Feng, Wenlong Hou, Guoqi Yu +4

Missing modality imputation aims to synthesize unobserved modalities from observed ones. Existing methods treat each modality as living on its own latent manifold, forcing the generator to learn a long, unstructured jump between them. We present SphereFlow, which takes a fundamentally different view: by projecting all modalities into a shared hyperspherical latent space via a frozen self-supervised encoder, cross-modal imputation reduces to short-range geometric transport between nearby points on the sphere. Realizing this idea with flow matching, however, exposes two geometric conflicts: the standard Gaussian noise source is catastrophically mismatched with the unit-norm data manifold, and the linear interpolation path departs the sphere surface into a region where the decoder has no training signal. We resolve both with simple, geometry-aware modifications: replacing the noise source with the observed-modality latent so that the velocity field learns only the cross-modal displacement, and training the decoder with a time-weighted loss that extends its domain to the near-surface region traversed by the flow. We prove that this data-as-source formulation reduces the worst-case…