PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers
cs.LG, cs.CE
Submitted: 2026-09-17
Updated: 2026-09-17
Comments: 32 pages, 10 figures, 21 tables; the code is available at https://github.com/neuraloperator/PosteriorBench
Code: https://github.com/neuraloperator/PosteriorBench
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- Score-Based Generative Modeling through Stochastic Differential Equations
- Diffusion Posterior Sampling for General Noisy Inverse Problems
- A Survey on Diffusion Models for Inverse Problems
- Fourier Neural Operator for Parametric Partial Differential Equations
- DiffusionPDE: Generative PDE-Solving Under Partial Observation
- Decoupled Diffusion Sampling for Inverse Problems on Function Spaces
- Monte Carlo guided Diffusion for Bayesian linear inverse problems
- DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
- Transformer for Partial Differential Equations' Operator Learning
- Neural Inverse Operators for Solving PDE Inverse Problems
- Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model
- A Variational Perspective on Solving Inverse Problems with Diffusion Models
- A Statistical Benchmark for Diffusion Posterior Sampling Algorithms
- Generative Latent Diffusion Model for Inverse Modeling and Uncertainty Analysis in Geological Carbon Sequestration
- Neural Operators with Localized Integral and Differential Kernels
Related papers
- Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
- AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
- Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
- Convergence issues in Relational Concept Analysis based on AOC-posets
- Beliefs Beyond Posteriors: Local-Consistency Optimisation for Bayesian Neural Networks
- Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks