mlsanityData to 7 Oct 2026

Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problems

arXiv 2303.15845 ↗First posted 28 Mar 2023cs.LG math.ST stat.THcited by 12

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Abstract (arXiv)

Conditional generative models became a very powerful tool to sample from Bayesian inverse problem posteriors. It is well-known in classical Bayesian literature that posterior measures are quite robust with respect to perturbations of both the prior measure and the negative log-likelihood, which includes perturbations of the observations. However, to the best of our knowledge, the robustness of conditional generative models with respect to perturbations of the observations has not been investigated yet. In this paper, we prove for the first time that appropriately learned conditional generative models provide robust results for single observations.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 36 of its 60 references that are in the map. First posted on arXiv 28 Mar 2023.

Builds on

36 of 60 references.

References · 36

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24 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 4; 2025: 2; 2026: 1.

12 papers.

  1. 2024Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matchingcited by 34
  2. 2023Posterior Sampling Based on Gradient Flows of the MMD with Negative Distance Kernelcited by 25
  3. 2023Adversarial robustness of amortized Bayesian inferencecited by 17
  4. 2023Learning from small data sets: Patch-based regularizers in inverse problems for image reconstructioncited by 9
  5. 2023NF-ULA: Langevin Monte Carlo with Normalizing Flow Prior for Imaging Inverse Problemscited by 4
  6. 2023Y-Diagonal Couplings: Approximating Posteriors with Conditional Wasserstein Distancescited by 3
  7. 2024A Likelihood Based Approach to Distribution Regression Using Conditional Deep Generative Modelscited by 3
  8. 2024Learning conditional distributions on continuous spacescited by 2
  9. 2025Provable Mixed-Noise Learning with Flow-Matchingcited by 2
  10. 2025A Mathematical Explanation of Transformerscited by 2
  11. 2024Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overviewcited by 1
  12. 2026Graph-Informed Adversarial Modeling: Infimal Subadditivity of Interpolative Divergencescited by 0