Flow-Based Generative Modeling

Flow-based generative modeling represents generation as a transformation of probability mass, often by integrating a continuous-time velocity field from noise to data or composing invertible normalizing-flow layers. Flow matching and rectified flow train velocity fields by regression along selected paths; optimal-transport couplings, stochastic interpolants, discrete Markov flows, and flow maps extend the toolkit to different data types and sampling budgets. Researchers apply these methods to images, language, molecules, physical fields, and robot actions, assessing fidelity and diversity alongside likelihood, constraint satisfaction, calibration, and runtime. A central challenge is achieving one- or few-step generation without sacrificing quality or mode coverage, while improving path design, robustness, geometric and physical consistency, and theoretical guarantees.