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Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference

arXiv 2006.06755 ↗First posted 11 Jun 2020stat.ML cs.LG stat.COcited by 40

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Abstract (arXiv)

We present a novel framework for conditional sampling of probability measures, using block triangular transport maps. We develop the theoretical foundations of block triangular transport in a Banach space setting, establishing general conditions under which conditional sampling can be achieved and drawing connections between monotone block triangular maps and optimal transport. Based on this theory, we then introduce a computational approach, called monotone generative adversarial networks (M-GANs), to learn suitable block triangular maps. Our algorithm uses only samples from the underlying joint probability measure and is hence likelihood-free. Numerical experiments with M-GAN demonstrate accurate sampling of conditional measures in synthetic examples, Bayesian inverse problems involving ordinary and partial differential equations, and probabilistic image in-painting.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Jun 2020.

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Citing papers per year: 2022: 1; 2023: 6; 2024: 12; 2025: 11; 2026: 10.

40 papers.

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  1. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensionscited by 37
  2. 2024Sampling in Unit Time with Kernel Fisher-Rao Flowcited by 27
  3. 2023Conditional Optimal Transport on Function Spacescited by 26
  4. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 24
  5. 2023Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inferencecited by 19
  6. 2024Score-based generative models are provably robust: an uncertainty quantification perspectivecited by 14
  7. 2025Flow Matching with Semidiscrete Couplingscited by 12
  8. 2024ASPIRE: Iterative Amortized Posterior Inference for Bayesian Inverse Problemscited by 11
  9. 2023Nonlinear Filtering with Brenier Optimal Transport Mapscited by 10
  10. 2024Conditional simulation via entropic optimal transport: Toward non-parametric estimation of conditional Brenier mapscited by 9
  11. 2025Probabilistic operator learning: generative modeling and uncertainty quantification for foundation models of differential equationscited by 9
  12. 2023A generative flow for conditional sampling via optimal transportcited by 7
28 more
  1. 2025Bifidelity Parameter Estimation Using Conditional Diffusion Modelscited by 7
  2. 2024Conditional score-based diffusion models for solving inverse problems in mechanicscited by 6
  3. 2022Generative Bayesian Inference with GANscited by 5
  4. 2024Diffeomorphic Measure Matching with Kernels for Generative Modelingcited by 4
  5. 2024Expected information gain estimation via density approximations: Sample allocation and dimension reductioncited by 4
  6. 2025Verification and Validation for Trustworthy Scientific Machine Learningcited by 4
  7. 2025A friendly introduction to triangular transportcited by 4
  8. 2024Solving High-dimensional Inverse Problems Using Amortized Likelihood-free Inference with Noisy and Incomplete Datacited by 3
  9. 2025Iterative Flow Matching: Path Correction and Gradual Refinement for Enhanced Generative Modelingcited by 3
  10. 2025Conditional Flow Matching for Bayesian Posterior Inferencecited by 3
  11. 2024Schr"odinger bridge based deep conditional generative learningcited by 2
  12. 2025Proximal optimal transport divergencescited by 2
  13. 2026Error Analysis of Bayesian Inverse Problems with Generative Priorscited by 2
  14. 2023Learning to sample in Cartesian MRIcited by 1
  15. 2024Generative Conditional Distributions by Neural (Entropic) Optimal Transportcited by 1
  16. 2025Geometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Latercited by 1
  17. 2026Conditional Sampling via Wasserstein Autoencoders and Triangular Transportcited by 1
  18. 2024Preserving linear invariants in ensemble filtering methodscited by 0
  19. 2025One-shot Conditional Sampling: MMD meets Nearest Neighborscited by 0
  20. 2025Bridging Simulators with Conditional Optimal Transportcited by 0
  21. 2026Coupling-Informed Transport Maps for Bayesian Filtering in Nonlinear Dynamical Systemscited by 0
  22. 2026Energy-based Transport for Amortized Bayesian Inferencecited by 0
  23. 2026A transition-density-based operator learning method for Fokker-Planck equations with various initial conditionscited by 0
  24. 2026Amortized quadrature for posterior expectations in inverse problemscited by 0
  25. 2026Generative models for simulation based filtering: Formulations and Empirical Comparisonscited by 0
  26. 2026Approximating Measures on Function Spaces: Transport and Truncationcited by 0
  27. 2026One-Step Generative Surrogate Models via Block-Triangular Joint Driftingcited by 0
  28. 2026Generative Priors Conditioned on Natural Language for Bayesian Inversion in PDEscited by 0