Flow Matching (Lipman et al. 2022) trains a vector field v_t(x) to transport samples from a simple source distribution p_0 (Gaussian) to a complex target p_1. The key insight: define conditional flows φ_t(x|x_1) = (1-t)·x_0 + t·x_1 (straight lines from noise to data), then regress on the marginal vector field. Unlike diffusion models, flow matching uses straight trajectories (ODE not SDE), enabling fast sampling with fewer function evaluations. The probability path is p_t = (1-t)·p_0 + t·p_1 at each time, and the trained field generates samples by integrating dx/dt = v_t(x).