The poor signal-to-noise problem -manifest as a large relative error in Euclidean correlators obtained from lattice Monte Carlo (MC) simulations—is endemic to lattice QCD.  An analysis of the spectral decomposition of the correlator variance suggests the problem is unavoidable.  I will show that evaluating the correlator as the derivative of a one-point function bypases the argument of the variance growth.  Although this derivative can be estimated in several ways, one particular technique "stochastic automatic differentiation" eliminates the signal-to-noise problem entirely, at least in scalar field theories.  The stochastic process is not guaranteed to converge in general, and gauge theories remain delicate, but these ideas may yet yield practical tools for QCD, or at least an interesting discussion!