  Devising optimal interventions for diffusive systems often requires the
solution of the Hamilton-Jacobi-Bellman (HJB) equation, a nonlinear backward
partial differential equation (PDE), that is, in general, nontrivial to solve.
Existing control methods either tackle the HJB directly with grid-based PDE
solvers, or resort to iterative stochastic path sampling to obtain the
necessary controls. Here, we present a framework that interpolates between
these two approaches. By reformulating the optimal interventions in terms of
logarithmic gradients ( scores ) of two forward probability flows, and by
employing deterministic particle methods for solving Fokker-Planck equations,
we introduce a novel fully deterministic framework that computes the required
optimal interventions in one shot.
