Physics-Informed Social Diffusion: Generative Modeling of Innovation Spread via Hybrid Physical-Social Diffusion Processes

While Guidolin & Manfredi (2022) review mathematical models of social innovation diffusion, and Lee et al. (2024) explore physical systems via generative models, these domains remain largely separate. This idea proposes a synthesis: construct a generative diffusion model that captures both physical (e.g., spatial, thermodynamic) and social (e.g., network, word-of-mouth, adoption) processes. For example, the model could simulate how an innovation spreads through populations embedded in a physical landscape, with both spatial constraints and social interactions, using training signals from both domains. This could be applied to epidemiology, marketing, or policy intervention design, and would be a significant leap from current models that treat social and physical diffusion separately. Domain-informed constraints (Zampini et al., 2025) could be incorporated to ensure realistic simulation of both physical and social laws.

References:

1. Training-Free Constrained Generation With Stable Diffusion Models. S. Zampini, Jacob Christopher, Luca Oneto, Davide Anguita, Ferdinando Fioretto (2025). arXiv.org.
2. Thermodynamic fidelity of generative models for Ising system. Brian H. Lee, Kat Nykiel, Ava E. Hallberg, Brice Rider, Alejandro Strachan (2024). Journal of Applied Physics.
3. Innovation Diffusion Processes: Concepts, Models, and Predictions. M. Guidolin, P. Manfredi (2022). Annual Review of Statistics and Its Application.