Combining spatially resolved X-ray Laue diffraction with atomic-scale simulations, we observe how ion-irradiated tungsten undergoes a series of non-linear structural transformations with increasing irradiation exposure. Nanoscale defect-induced deformations accumulating above 0.02 displacements per atom (dpa) lead to highly fluctuating strains at ~0.1 dpa, collapsing into a driven quasi-steady structural state above ~1 dpa. The driven asymptotic state is characterized by finely dispersed defects coexisting with an extended dislocation network and exhibits positive volumetric swelling but negative lattice strain.