How to make random sampling escape traps faster?

Adding carefully chosen probability currents to a diffusion process can dramatically speed up sampling without changing what distribution you're sampling from — like stirring a liquid to help it mix faster. This paper casts those currents as gauge fields in a quantum-mechanics-style operator formalism, revealing that popular optimizers like Adam are secretly choosing these currents implicitly. An actor-critic learning procedure finds the optimal finite-strength current, confirmed exactly on Gaussian and double-well test cases.