Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Why Stochastic Thermodynamics of Machine Learning?
- Part IPreliminaries
- Part IIDiscrete-Time Stochastic Dynamics
- 4Latent Variable Models and Graphical Models
- 5Thermodynamics of Probabilistic Machine Learning
- 6Belief Propagation
- 7The Variational Autoencoder
- 8Normalizing Flows
- 9Markov Processes and Time Reversal
- 10Stochastic Thermodynamics
- 11Markov Chain Monte Carlo
- 12Sequential Importance Sampling
- 13Variational Diffusion Models
- 14Schrödinger Bridges
- 15Optimal Control
- 16Generative Flow Networks
- 17Fluctuation Theorems
- 18Free Energy Estimation
- 19Escorted Free Energy Estimations and Fluctuation Theorems
- 20Hybrid Stochastic Flows and Surjective Flows
- Part IIIContinuous-Time Probabilistic Dynamics
- 21Stochastic Thermodynamics from the Fokker–Planck Equation
- 22Optimal Transport and Schrödinger Bridge
- 23Continuous Normalizing Flows and Flow Matching
- Part IVEpilogue
- Bibliography
- Index
23 - Continuous Normalizing Flows and Flow Matching
from Part II - Discrete-Time Stochastic Dynamics
Published online by Cambridge University Press: 20 July 2026
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- Why Stochastic Thermodynamics of Machine Learning?
- Part IPreliminaries
- Part IIDiscrete-Time Stochastic Dynamics
- 4Latent Variable Models and Graphical Models
- 5Thermodynamics of Probabilistic Machine Learning
- 6Belief Propagation
- 7The Variational Autoencoder
- 8Normalizing Flows
- 9Markov Processes and Time Reversal
- 10Stochastic Thermodynamics
- 11Markov Chain Monte Carlo
- 12Sequential Importance Sampling
- 13Variational Diffusion Models
- 14Schrödinger Bridges
- 15Optimal Control
- 16Generative Flow Networks
- 17Fluctuation Theorems
- 18Free Energy Estimation
- 19Escorted Free Energy Estimations and Fluctuation Theorems
- 20Hybrid Stochastic Flows and Surjective Flows
- Part IIIContinuous-Time Probabilistic Dynamics
- 21Stochastic Thermodynamics from the Fokker–Planck Equation
- 22Optimal Transport and Schrödinger Bridge
- 23Continuous Normalizing Flows and Flow Matching
- Part IVEpilogue
- Bibliography
- Index
Summary
Congratulations, you have made it to the end! I hope you got the main message of this book: that there is a remarkable connection between the field of nonequilibrium thermodynamics (or a subfield known as stochastic thermodynamics) and probabilistic machine learning (and its subfield now known as generative AI). The mathematics that is used to generate beautiful videos of dogs playing in the snow is the same as that of describing thermodynamic systems such as solids, liquids, and gases out of equilibrium.
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- Generative AI and Stochastic ThermodynamicsA Tale of Free Energies, pp. 248 - 262Publisher: Cambridge University PressPrint publication year: 2026
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