This paper provides an integrated theoretical understanding of the operation of the generative-diffusion model. We analyze the generative-diffusion model by linking dynamical, information-theoretic, and thermodynamic properties within a unified mathematical framework. We show that the conditional entropy generation rate (generation bandwidth) during the generation process is directly related to the divergence of the vector field of the score function. This divergence is associated with trajectory bifurcation and generation bifurcation, and is characterized by symmetry-breaking phase transitions in the energy landscape. We conclude that the generation process is fundamentally driven by controlled, noise-induced symmetry breaking, with peaks in information transfer corresponding to critical transitions between possible outcomes. The score function acts as a dynamic nonlinear filter that modulates the bandwidth of the noise by suppressing fluctuations that are incompatible with the data.