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We first extend the classic Tweedie’s formula to a wider range of distributions, then derive a new identity that links the (Stein) score under a generalized Gaussian (energy model) noise to the gradient of a matched Energy Score (a scoring rule), connecting two seemingly disparate approaches to generative modeling and serving as an analog to the classic Tweedie’s formula. Among other things, this represents a novel score matching estimator, as well as enables energy-score-based denoising models to be plugged into standard diffusion pipelines, but with heavy‑tailed noise.

Modeling the translation and review processes as zero-inflated fat-tailed distributions, we show how to extract useful information on translators’ reliability with as little as one review per translation.