Learning Generative Dynamics with Soft Path-Law Constraints: A McKean-Vlasov FBSDE Approach
The method learns stochastic dynamics by formulating generation as a McKean-Vlasov control problem constrained by soft energy terms. It uses intermediate distributional observations to generate running law-gradient forces, while endpoint observations act as terminal conditions. This provides a principled way to select a path law that balances marginal fidelity with control effort, enabling the generation of structured trajectories.