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The Information Dynamics of Generative Diffusion

Created by
  • Haebom

Author

Luca Ambrogioni

Outline

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.

Takeaways, Limitations

Takeaways: We present a new theoretical framework that integrates the operational principles of the generation-diffusion model from dynamical, information-theoretic, and thermodynamic perspectives. By elucidating the relationship between information transfer and symmetry breaking during the generation process, we provide a deeper understanding of the model's operating mechanism. By clarifying the role of the score function, we provide directions for model improvement and new model design.
Limitations: The proposed theoretical framework lacks experimental validation. Further research is needed to determine its applicability and generalizability to realistic generative diffusion models. Further analysis is needed to determine its applicability to complex, high-dimensional data and its limitations.
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