The analysis of diffusive energy spreading in quantized chaotic driven systems, leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation a driven chaotic system exhibits stochastic-like diffusion in energy space with a coefficient D that is proportional to the intensity ϵ^2 of the driving. In the corresponding quantized problem the coherent transitions are characterized by a generalized Wigner time t_ϵ, and a self-generated (intrinsic) dephasing process leads to non-linear dependence of D on ϵ^2.