Dynamical Measure Transport

Dynamical measure transport aims to efficiently sample from complex probability distributions by mapping a simpler, known distribution to the target distribution via a continuous-time transformation. Current research focuses on learning these transformations using neural networks, particularly physics-informed neural networks, and stochastic interpolants, often within variational frameworks to optimize the transport process. This approach improves upon existing sampling methods like Markov Chain Monte Carlo by offering enhanced mode coverage and efficiency, with applications in generative modeling, including conditional generation and multimarginal problems relevant to tasks such as style transfer and data augmentation.