Localized Subspace Source Adaptation for Flow Matching

Spatially varying local subspaces are not captured by the global statistics commonly used to adapt Flow Matching (FM) sources. We study which target information should be retained in the initial distribution without changing the probability path or FM objective. We introduce Localized Subspace Source Adaptation (LSSA), a source-only adaptation that represents target regions with multiple anchors and orients Gaussian-mixture components using local PCA projectors. LSSA retains dominant regional directions without reproducing local covariance magnitudes, while a shared variance budget controls total scale and an isotropic residual preserves ambient variation. Across structured toy distributions, scientific data, CLIP and HyCoCLIP embedding generation, LSSA consistently improves distributional fidelity, and competitive in MNIST, over standard Gaussian and statistic-specific source baselines. It achieves the lowest SWD and MMD in the evaluated scientific and embedding-generation settings and improves over the Gaussian in both pixel and VAE-latent MNIST generation. These results show that explicitly modeling localized subspace structure is an effective source-design principle in the evaluated structured and representation spaces for FM.