mlsanityData to 7 Oct 2026

A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios

arXiv 2512.23748 ↗First posted 26 Dec 2025cs.LG math.PR stat.MLcited by 1

On the map: Diffusion models → Flow matching, time series and science

Abstract (arXiv)

For complex simulation problems, inferring parameters often precludes the use of classical likelihood-based techniques due to intractable likelihoods. Simulation-based inference (SBI) methods offer a likelihood-free approach to directly learn posterior distributions p(bftheta mid xobs) from simulator outputs. Recently, diffusion models have emerged as promising tools for SBI, addressing limitations of earlier neural methods such as neural likelihood/posterior estimation and normalizing flows. This review examines diffusion-based SBI from first principles to applications, emphasizing robustness in three non-ideal data scenarios common to scientific computing: model misspecification (simulator-reality mismatch), unstructured or infinite-dimensional observations, and missing data. We synthesize mathematical foundations and survey eight methods addressing these challenges, such as conditional diffusion for irregular data, guided diffusion for prior adaptation, sequential and factorized approaches for efficiency, and consistency models for fast sampling. Throughout, we maintain consistent notation and emphasize conditions required for accurate posteriors. We conclude with open problems and applications to geophysical uncertainty quantification, where these challenges are acute.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 44 of its 63 references that are in the map. First posted on arXiv 26 Dec 2025.

Builds on

44 of 63 references.

Closest ancestors · 3

Same direction, newest first

  1. 2023Consistency Models for Scalable and Fast Simulation-Based Inference9 Dec
  2. 2023Flow Matching for Scalable Simulation-Based Inference26 May
  3. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation7 Jul

Other references · 41

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2022Scalable Diffusion Models with Transformerscited by 5,931
  5. 2022Classifier-Free Diffusion Guidancecited by 5,717
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  11. 2019The frontier of simulation-based inferencecited by 490
  12. 2018Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flowscited by 217
29 more
  1. 2019Automatic Posterior Transformation for Likelihood-Free Inferencecited by 216
  2. 2021Conditional Image Generation with Score-Based Diffusion Modelscited by 195
  3. 2021Benchmarking Simulation-Based Inferencecited by 160
  4. 2020BayesFlow: Learning complex stochastic models with invertible neural networkscited by 139
  5. 2023Score-based Data Assimilationcited by 91
  6. 2024All-in-one simulation-based inferencecited by 71
  7. 2022Conditional Simulation Using Diffusion Schr"odinger Bridgescited by 58
  8. 2016Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimationcited by 50
  9. 2022Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Modelscited by 50
  10. 2022Diffusion Generative Models in Infinite Dimensionscited by 49
  11. 2022Compositional Score Modeling for Simulation-based Inferencecited by 46
  12. 2022Robust Neural Posterior Estimation and Statistical Model Criticismcited by 45
  13. 2020A Survey on Principles, Models and Methods for Learning from Irregularly Sampled Time Seriescited by 42
  14. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensionscited by 37
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  17. 2023Bayesian Synthetic Likelihoodcited by 29
  18. 2021A Trust Crisis In Simulation-Based Inference? Your Posterior Approximations Can Be Unfaithfulcited by 27
  19. 2022Spectral Diffusion Processescited by 24
  20. 2024Amortized Probabilistic Conditioning for Optimization, Simulation and Inferencecited by 22
  21. 2023Neural Diffusion Modelscited by 20
  22. 2023Sensitivity-Aware Amortized Bayesian Inferencecited by 20
  23. 2022Graphically Structured Diffusion Modelscited by 11
  24. 2023Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probabilitycited by 10
  25. 2024Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigationcited by 8
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  29. 2025ConDiSim: Conditional Diffusion Models for Simulation Based Inferencecited by 2

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Citing papers per year: 2025: 1.

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