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The classical dynamics of collisionless cold dark matter, commonly describedby fluid variables or a phase-space distribution, can be captured in a singlesemiclassical wavefunction. We illustrate how classical multi-streaming createswave interference in a toy model corresponding to the dynamics of theZel'dovich approximation and link it to diffraction optics. Wave interferencedresses the classical skeleton of cold dark matter with universal features akinto the physical imprints of wavelike (or fuzzy) dark matter. We untangle thiswave interference to obtain single-stream wavefunctions corresponding to theclassical fluid streams, by writing the wavefunction in an integral form. Ourwave decomposition captures the full phase-space information and isolates themulti-stream phenomena related to vorticity and velocity dispersion. We linkthe wave interference features of our system to the standard forms ofdiffraction catastrophe integrals, which produce bright caustics in opticalfields analogous to the cold dark matter density field. Our two complementarydescriptions of dark matter wave-fields present rich universal features thatcan unlock new ways of modelling and probing wavelike dark matter on the scalesof the cosmic web.

Making (dark matter) waves: Untangling wave interference for multi-streaming dark matter