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The density structure of the interstellar medium determines where stars form and release energy, momentum and heavy elements, driving galaxy evolution1-4. Density variations are seeded and amplified by gas motion, but the exact nature of this motion is unknown across spatial scales and galactic environments5. Although dense star-forming gas probably emerges from a combination of instabilities6,7, convergent flows8 and turbulence9, establishing the precise origin is challenging because it requires gas motion to be quantified over many orders of magnitude in spatial scale. Here we measure10-12 the motion of molecular gas in the Milky Way and in nearby galaxy NGC 4321, assembling observations that span a spatial dynamic range 10-1-103 pc. We detect ubiquitous velocity fluctuations across all spatial scales and galactic environments. Statistical analysis of these fluctuations indicates how star-forming gas is assembled. We discover oscillatory gas flows with wavelengths ranging from 0.3-400 pc. These flows are coupled to regularly spaced density enhancements that probably form via gravitational instabilities13,14. We also identify stochastic and scale-free velocity and density fluctuations, consistent with the structure generated in turbulent flows9. Our results demonstrate that the structure of the interstellar medium cannot be considered in isolation. Instead, its formation and evolution are controlled by nested, interdependent flows of matter covering many orders of magnitude in spatial scale.