Probability Flow

Probability flow describes the movement of probability density over time, a concept central to understanding and manipulating probability distributions in various fields. Current research focuses on leveraging optimal transport theory and neural networks to model and predict this flow, particularly within the context of diffusion models and normalizing flows for tasks like image generation and time series forecasting. These advancements enable more efficient sampling, improved estimations of thermodynamic quantities like Gibbs free energy, and enhanced predictions of dynamic systems, impacting diverse areas from statistical physics to social network analysis. The development of accurate and efficient probability flow models is driving progress in both theoretical understanding and practical applications of probability distributions.