  Motivated by the increasing popularity of overparameterized Stochastic
Differential Equations (SDEs) like Neural SDEs, Wang, Blanchet and Glynn
recently introduced the generator gradient estimator, a novel unbiased
stochastic gradient estimator for SDEs whose computation time remains stable in
the number of parameters. In this note, we demonstrate that this estimator is
in fact an adjoint state method, an approach which is known to scale with the
number of states and not the number of parameters in the case of Ordinary
Differential Equations (ODEs). In addition, we show that the generator gradient
estimator is a close analogue to the exact Integral Path Algorithm (eIPA)
estimator which was introduced by Gupta, Rathinam and Khammash for a class of
Continuous-Time Markov Chains (CTMCs) known as stochastic chemical reactions
networks (CRNs).
