mlsanityData to 14 Oct 2026

Error Analysis of Bayesian Inverse Problems with Generative Priors

arXiv 2601.17374 ↗First posted 24 Jan 2026stat.ML cs.LG cs.NAcited by 2

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Abstract (arXiv)

Data-driven methods for the solution of inverse problems have become widely popular in recent years thanks to the rise of machine learning techniques. A popular approach concerns the training of a generative model on additional data to learn a bespoke prior for the problem at hand. In this article we present an analysis for such problems by presenting quantitative error bounds for minimum Wasserstein-2 generative models for the prior. We show that under some assumptions, the error in the posterior due to the generative prior will inherit the same rate as the prior with respect to the Wasserstein-1 distance. We further present numerical experiments that verify that aspects of our error analysis manifests in some benchmarks followed by an elliptic PDE inverse problem where a generative prior is used to model a non-stationary field.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 42 of its 66 references that are in the map. First posted on arXiv 24 Jan 2026.

Builds on

42 of 66 references.

References · 42

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30 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026On the role of memorization in learned priors for geophysical inverse problemscited by 1
  2. 2026Generative Priors Conditioned on Natural Language for Bayesian Inversion in PDEscited by 0