Adjoint Schrödinger Flow Map Sampler

Sampling from distribution specified by unnormalized energy function can be amortized with diffusion sampler, but generating samples requires numerical integration of the learned stochastic dynamics. This paper introduces Adjoint Schrödinger Flow Map (ASFM) Sampler, which learns deterministic finite time map for energy based sampling. ASFM combines the bridge coupling obtained during adjoint training with the adjoint signal to construct a probability flow velocity target using energy evaluations alone. This target is then used to train a finite time map that reproduces the marginal evolution of the learned bridge. The method requires neither target samples nor a separately trained teacher. Experiments show that composing a few learned maps reproduces the sampling quality of numerical probability flow integration.