Abstract We use the single-dish radio telescope Five-hundred meter Aperture Spherical Telescope (FAST) to map the H i in the tidally interacting NGC 4631 group with a resolution of 3.′24 (7 kpc), reaching a 5σ column density limit of 10^17.9 cm⁻² assuming a line width of 20 km s⁻¹. Taking the existing interferometric H i image from the Hydrogen Accretion in LOcal GAlaxieS project of Westerbork Synthesis Radio Telescope as a reference, we are able to identify and characterize a significant excess of large-scale, low-density, and diffuse H i in the group. This diffuse H i extends more than 120 kpc across, and accounts for more than one-fourth of the total H i detected by FAST in and around the galaxy NGC 4631. In the region of the tidal tails, the diffuse H i has a typical column density above 10^19.5 cm⁻², and is highly turbulent with a velocity dispersion of around 50 km s⁻¹. It increases in column density with the dense H i, and tends to be associated with the kinematically hotter part of the dense H i. Through simple modeling, we find that the majority of the diffuse H i in the tail region is likely to induce cooling out of the hot intragalactic medium (IGM) instead of evaporating or being radiatively ionized. Given these relations of gas in different phases, the diffuse H i may represent a condensing phase of the IGM. Ongoing and past active tidal interactions may have produced the wide-spreading H i distribution, and triggered the gas accretion to NGC 4631 through the phase of the diffuse H i.