Conditional Flow Matching

Conditional Flow Matching learns a time-dependent velocity field that carries samples from a source distribution, often noise, toward a target distribution given conditions such as an image, measurement, or physical state. Methods improve this transport with optimal-transport couplings, tailored interpolation paths and schedules, and physics or task-specific constraints; applications include image generation, inverse problems, forecasting, and biological dynamics. Evaluation spans image benchmarks such as CIFAR-10 and ImageNet, as well as PDE, medical-imaging, and single-cell settings, with work also targeting faster sampling through better solvers and distillation. A central tension is balancing sample quality and reliable uncertainty or physical fidelity against training and inference cost, while clarifying when the flow-matching objective supports calibrated likelihoods or posterior estimates.