Two-dimensional excitons formed in quantum materials such as monolayer transition-metal dichalcogenides and their strong light-matter interaction have attracted unrivalled attention by the research community due to their extraordinarily large oscillator strength as well as binding energy, and the inherent spin-valley locking. Semiconducting few-layer and monolayer materials with their sharp optical resonances such as WSe2 have been extensively studied and envisioned for applications in the weak as well as strong light-matter coupling regimes, for effective nano-laser operation with various different structures, and particularly for valleytronic nanophotonics motivated by the circular dichroism... Many of these applications, which may benefit heavily from the two-dimensional electronic quasiparticle's properties in such films, require controlling, manipulating and first of all understanding the nature of the optical resonances that are attributed to exciton modes. While theory and previous experiments have provided unique methods to the characterization and classification efforts regarding the band structure and optical modes in 2D materials, here, we directly measure the quasiparticle energy-momentum dispersion for the first time. Our results for single-layer WSe2 clearly indicate an emission regime predominantly governed by free excitons, i.e. Coulomb-bound electron-hole pairs with centre-of-mass momentum and corresponding effective mass. Besides uniquely evidencing the existence of free excitons at cryogenic temperatures optically, the fading of the dispersive character for increased temperatures or excitation densities reveals a transition to a regime with profound role of charge-carrier plasma or localized excitons regarding its emission, debunking the myth of free-exciton emission at elevated temperatures. (read more)