Complex Ginzburg-Landau equation (CGLE) is a universal amplitude equation governing the dynamics of phenomena unfolding in far-from-equilibrium conditions. It was recently argued that CGLE emerges from primordial dimensional fluctuations acting in the far ultraviolet sector of field theory and primordial cosmology. Here we show that classical Maxwell, Dirac and non-Abelian field theories can be derived directly from a generalized version of CGLE without invoking a Lagrangian or variational principle. Demanding that CGLE preserves local coherence under continuous internal transformations, we introduce a natural covariant derivative whose connection acts as a gauge field. The commutator of these covariant derivatives defines a curvature tensor that reproduces the familiar structure of Maxwell and Yang—Mills field strengths, while a first-order, spinor generalization of CGLE yields Dirac-type dynamics. In a nutshell, classical field theories naturally emerge from demanding local coherence invariance of the generalized CGLE.