We propose score-based diffusion framework with explicit G-modeling, a nonparametric empirical Bayes method that achieves near-parametric score estimation guarantees and state-of-the-art denoising for multivariate heteroscedastic Gaussian mixtures.

We introduce a modular matrix factorization framework called "covariate-moderated empirical Bayes matrix factorization" (cEBMF) that can leverage side information to improve the factorization through the use of adaptive priors.