2025ApJ...993....4L

Unraveling the multiphase structure of the diffuse interstellar medium as traced by neutral hydrogen (H I) is essential to understanding the lifecycle of the Milky Way. However, H I phase separation is a challenging and underconstrained problem. The neutral gas phase distribution is often inferred from the spectral line structure of H I emission. In this work, we develop a data-driven phase-separation method that extracts H I phase structure solely from the spatial morphology of H I emission intensity structures. We combine scattering spectra (SS) statistics with a Gaussian-mixture variational autoencoder model to (1) derive an interpretable statistical model of different H I phases from their multiscale morphological structures, and (2) we use this model to decompose the 2D channel maps of GALFA-H I emission in diffuse high-latitude (∣b∣ > 30°) regions over narrow velocity channels (Δv = 3 km s^–1) into cold neutral medium (CNM), warm neutral medium (WNM), and noise components. We integrate our CNM map over velocity channels to compare it to an existing map produced by a spectrum-based method. We find that the two maps are highly correlated, but ours recovers more spatially coherent structures at small scales. Our work illustrates and quantifies a clear physical connection between the H I morphology and H I phase structure, and it unlocks a new avenue for improving future phase-separation techniques by making use of both H I spectral and spatial information to decompose H I in 3D position-position-velocity space. These results are consistent with a physical picture where processes that drive H I phase transitions also shape the morphology of H I gas, imprinting a sparse, filamentary CNM that forms out of a diffuse, extended WNM.