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Abstract Next-generation radio telescopes will provide unprecedented data volumes of the neutral hydrogen (HI) distribution across cosmic time. The spatial and kinematic distribution of H i is a biased tracer of the underlying matter field, and as such contains information on the distribution of dark matter over a wide range of scales. Extracting dark matter properties from H i, however, is non-trivial because baryonic processes linked to galaxy formation significantly modify the H i distribution. Additionally, methods that use empirical relations, often calibrated via numerical simulations, do not use the full field-level information to model the complex relation between H i and dark matter. We use the recently introduced EMBER-2 model to directly predict dark matter distributions from H i tracers over a wide redshift range, z = 0 − 6. After training on cosmological galaxy formation simulations run with FIRE-2, our method accurately recovers key statistics, including dark matter mass fractions, surface density profiles and cross-correlations, where the latter are reconstructed at an accuracy of 20 % down to scales of k = 100 h/cMpc constituting a significant improvement over traditional approaches. The presented method may become a key ingredient in future inference pipelines as it can be readily integrated into downstream analysis tasks of radio surveys.