Abstract We present new ALMA observations of CO, CN, CS, HCN and HCO+ absorption seen against the bright and compact radio continuum sources of eight galaxies. Combined with archival observations, they reveal two distinct populations of molecular clouds, which we identify by combining CO emission and absorption profiles to unambiguously reveal each cloud’s direction of motion and likely location. In galaxy disks, we see clouds with low velocity dispersions, low line of sight velocities and a lack of any systemic inflow or outflow. In galactic cores, we find high velocity dispersion clouds inflowing at up to 550 km/s. This provides observational evidence in favour of cold accretion onto galactic centres, which likely contributes to the fuelling of active galactic nuclei. We also see a wide range in the CO(2-1)/CO(1-0) ratios of the absorption lines. This is likely the combined effect of hierarchical substructure within the molecular clouds and continuum sources which vary in size with frequency.