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The density structure of the interstellar medium (ISM) determines where stars form and release energy, momentum, and heavy elements, driving galaxy evolution. Density variations are seeded and amplified by gas motion, but the exact nature of this motion is unknown across spatial scale and galactic environment. Although dense star-forming gas likely emerges from a combination of instabilities, convergent flows, and turbulence, establishing the precise origin is challenging because it requires quantifying gas motion over many orders of magnitude in spatial scale. Here we measure the motion of molecular gas in the Milky Way and in nearby galaxy NGC 4321, assembling observations that span an unprecedented spatial dynamic range ($10^{-1}{-}10^3$ 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 likely form via gravitational instabilities. We also identify stochastic and scale-free velocity and density fluctuations, consistent with the structure generated in turbulent flows. Our results demonstrate that ISM structure cannot be considered in isolation. Instead, its formation and evolution is controlled by nested, interdependent flows of matter covering many orders of magnitude in spatial scale.