Energy-Tweedie generalizes Tweedie's formula from Gaussian to Gibbs noise distributions
umichigan · hf · 2026-11-10
A paper by Andrej Leban (University of Michigan) extends Tweedie's formula, which links denoising posterior means under Gaussian noise to Stein scores, to a broad class of Gibbs (energy-based) noise distributions, with the generalized Gaussian family as a running example. The Energy-Tweedie identity shows that when the denoising posterior is viewed through kernel scoring rules, the path derivative of a scoring rule defined by the noise potential recovers the Stein score of the noisy marginal, with propriety determined by the noise potential alone. Applications include score estimation, noise-parameter estimation and diffusion-style sampling.
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