Denoising Diffusion Monte Carlo Electron Densities with Physically Informed Variance Stabilization: From Fourier Filters to 3D UNETs

Abstract

Obtaining accurate electron densities is important for the fundamental description of molecular and condensed matter systems, as well as for the development of next-generation density functionals. Diffusion Monte Carlo (DMC), in particular, is known to produce benchmark-quality data; however, the predicted real-space electron densities contain substantial amounts of statistical noise. In this work, we study denoising approaches for DMC densities, judged on the basis of the information-theoretic Jensen-Shannon divergence. The denoising is facilitated by an approximate heteroscedastic to homoscedastic transformation leveraging the density functional theory density as a physical prior. We systematically compare a range of denoising techniques-including Fourier transform, regression, and 3D UNETs-on materials showing a wide range of density variations: carbon diamond, blue phosphorus, and rutile VO2. Our results indicate that simple flattened machine learning models and 2D image-based models introduce line artifacts and struggle to capture the full spatial correlation. In contrast, when using variance stabilization, regression methods outperform all others in both the high and low- noise limits across all materials considered. The best denoisers reduce the required cost of density-generating DMC simulations by 10-100x, providing a promising route forward for application in noise-sensitive tasks such as DFT functional inversion.