Nuclear Quantum Effects as a Denoising Problem

What the math gives to ML

The paper identifies a useful factorization of a target distribution into an arbitrary residual Boltzmann factor and a fully known quadratic context, with the latter represented by a Gaussian structure. For neural generative models, this suggests training a context-free denoiser once on the residual distribution and injecting mass, temperature, boundary-condition, or other quadratic changes analytically during sampling rather than conditioning or retraining the network. The transferable asset is an explicitly parameterized positive-semidefinite quadratic action whose score and covariance can be computed efficiently by linear algebra. A practical first test is a diffusion sampler for distributions of the form $p_K(x)\propto e^{-U(x)-x^\top Kx/2}$, comparing analytic quadratic score composition against separately conditioned models.