The Statistical Thermodynamics of Generative Diffusion Models: Phase Transitions, Symmetry Breaking, and Critical Instability
Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference, and stochastic calculus, in this paper we show that many aspects of t...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-03-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/27/3/291 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849341593658589184 |
|---|---|
| author | Luca Ambrogioni |
| author_facet | Luca Ambrogioni |
| author_sort | Luca Ambrogioni |
| collection | DOAJ |
| description | Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference, and stochastic calculus, in this paper we show that many aspects of these models can be understood using the tools of equilibrium statistical mechanics. Using this reformulation, we show that generative diffusion models undergo second-order phase transitions corresponding to symmetry breaking phenomena. We show that these phase transitions are always in a mean-field universality class, as they are the result of a self-consistency condition in the generative dynamics. We argue that the critical instability arising from these phase transitions lies at the heart of their generative capabilities, which are characterized by a set of mean-field critical exponents. Finally, we show that the dynamic equation of the generative process can be interpreted as a stochastic adiabatic transformation that minimizes the free energy while keeping the system in thermal equilibrium. |
| format | Article |
| id | doaj-art-34c04e75aa8d47b2b6ddde485921c83a |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-34c04e75aa8d47b2b6ddde485921c83a2025-08-20T03:43:36ZengMDPI AGEntropy1099-43002025-03-0127329110.3390/e27030291The Statistical Thermodynamics of Generative Diffusion Models: Phase Transitions, Symmetry Breaking, and Critical InstabilityLuca Ambrogioni0Donders Institute for Brain, Cognition and Behaviour, Radboud University, 6525 XZ Nijmegen, The NetherlandsGenerative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference, and stochastic calculus, in this paper we show that many aspects of these models can be understood using the tools of equilibrium statistical mechanics. Using this reformulation, we show that generative diffusion models undergo second-order phase transitions corresponding to symmetry breaking phenomena. We show that these phase transitions are always in a mean-field universality class, as they are the result of a self-consistency condition in the generative dynamics. We argue that the critical instability arising from these phase transitions lies at the heart of their generative capabilities, which are characterized by a set of mean-field critical exponents. Finally, we show that the dynamic equation of the generative process can be interpreted as a stochastic adiabatic transformation that minimizes the free energy while keeping the system in thermal equilibrium.https://www.mdpi.com/1099-4300/27/3/291generative diffusionstatistical physicsphase transitionsspontaneous symmetry breaking |
| spellingShingle | Luca Ambrogioni The Statistical Thermodynamics of Generative Diffusion Models: Phase Transitions, Symmetry Breaking, and Critical Instability Entropy generative diffusion statistical physics phase transitions spontaneous symmetry breaking |
| title | The Statistical Thermodynamics of Generative Diffusion Models: Phase Transitions, Symmetry Breaking, and Critical Instability |
| title_full | The Statistical Thermodynamics of Generative Diffusion Models: Phase Transitions, Symmetry Breaking, and Critical Instability |
| title_fullStr | The Statistical Thermodynamics of Generative Diffusion Models: Phase Transitions, Symmetry Breaking, and Critical Instability |
| title_full_unstemmed | The Statistical Thermodynamics of Generative Diffusion Models: Phase Transitions, Symmetry Breaking, and Critical Instability |
| title_short | The Statistical Thermodynamics of Generative Diffusion Models: Phase Transitions, Symmetry Breaking, and Critical Instability |
| title_sort | statistical thermodynamics of generative diffusion models phase transitions symmetry breaking and critical instability |
| topic | generative diffusion statistical physics phase transitions spontaneous symmetry breaking |
| url | https://www.mdpi.com/1099-4300/27/3/291 |
| work_keys_str_mv | AT lucaambrogioni thestatisticalthermodynamicsofgenerativediffusionmodelsphasetransitionssymmetrybreakingandcriticalinstability AT lucaambrogioni statisticalthermodynamicsofgenerativediffusionmodelsphasetransitionssymmetrybreakingandcriticalinstability |