The New Special Issue "The Statistical Physics of Generative Diffusion Models" is Open for Submission!

Guest Editor: Dr. Luca Ambrogioni (Radboud University)

Submit to the Special Issue: https://www.mdpi.com/journal/entropy/special_issues/Gener_Diffus_Model

Submission deadline: 31 March 2025

Special Issue Information: Generative diffusion models and related methods such as stochastic interpolants have become the state of the art in image and video generation. While these methods were inspired by the physics of out-of-equilibrium systems, recent work revealed deep connections between generative diffusion models and equilibrium statistical physics. In particular, it was shown that the generative diffusion process is punctuated by spontaneous symmetry breaking events that correspond to splits between semantic classes or visual features and are formally equivalent to mean-field critical phase transitions. These ‘speciation’ phase transitions correspond to critical windows where the generative process is maximally controllable. Another fascinating venue of research is the connection between generative diffusion models and associative memory networks such as (modern) Hopfield networks. For example, using Hopfield techniques, it has been shown that memorization in generative diffusion is the result of ‘glassy’ (i.e., disordered) phase transitions in the average free energy. The connections between spin glass sampling and generative diffusion have been further investigated using the concept of stochastic localization, which describes the (spontaneous) concentration of measure observed in generative diffusion sampling. These developments have the potential to drive a large inflow of physical theory and techniques to the study of generative machine learning models, which could lead to radical insights on the nature of learning and intelligence.

Given these fascinating developments, we are excited to launch a Special Issue aimed at connecting research in statistical physics and generative diffusion modeling. Authors are encouraged to submit their research to this Special Issue. Topics include, but are not limited to, the following:

• Theoretical analysis of generative diffusion processes;
• Connection between diffusion models and Hopfield networks;
• Statistical physics analysis of flow matching processes and stochastic interpolants;
• Theoretical analysis of prompt conditioning in generative diffusion;
• Differential geometry of diffusion latent manifolds;
• Acceleration of generative diffusion sampling using computational physics methods;
• Discrete generative diffusion processes;
• Connection between generative diffusion processes and spin glasses;
• Spontaneous symmetry breaking in equivariant generative diffusion models;
• Applications of generative diffusion to statistical physics problems;
• Stochastic localization processes;
• Statistical physics of consistency models;
• Applications of generative diffusion to econophysics and finance.