mlsanityData to 7 Oct 2026

Flow Matching for Scalable Simulation-Based Inference

arXiv 2305.17161 ↗First posted 26 May 2023cs.LGcited by 97

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

Abstract (arXiv)

Neural posterior estimation methods based on discrete normalizing flows have become established tools for simulation-based inference (SBI), but scaling them to high-dimensional problems can be challenging. Building on recent advances in generative modeling, we here present flow matching posterior estimation (FMPE), a technique for SBI using continuous normalizing flows. Like diffusion models, and in contrast to discrete flows, flow matching allows for unconstrained architectures, providing enhanced flexibility for complex data modalities. Flow matching, therefore, enables exact density evaluation, fast training, and seamless scalability to large architectures--making it ideal for SBI. We show that FMPE achieves competitive performance on an established SBI benchmark, and then demonstrate its improved scalability on a challenging scientific problem: for gravitational-wave inference, FMPE outperforms methods based on comparable discrete flows, reducing training time by 30% with substantially improved accuracy. Our work underscores the potential of FMPE to enhance performance in challenging inference scenarios, thereby paving the way for more advanced applications to scientific problems.

Key facts. Cited by 97 papers 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 45 of its 80 references that are in the map. First posted on arXiv 26 May 2023.

Builds on

45 of 80 references.

Closest ancestors · 2

Same direction, newest first

  1. 2022Flow Matching for Generative Modeling6 Oct
  2. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow7 Sep

Other references · 43

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  7. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  8. 2018Neural Ordinary Differential Equationscited by 3,733
  9. 2015Variational Inference with Normalizing Flowscited by 2,161
  10. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  11. 2021Cascaded Diffusion Models for High Fidelity Image Generationcited by 1,155
  12. 2016Group Equivariant Convolutional Networkscited by 1,154
31 more
  1. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  2. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  3. 2016Language Modeling with Gated Convolutional Networkscited by 688
  4. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
  5. 2019Neural Spline Flowscited by 590
  6. 2019The frontier of simulation-based inferencecited by 490
  7. 2016Revisiting Classifier Two-Sample Testscited by 258
  8. 2018Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flowscited by 217
  9. 2019Automatic Posterior Transformation for Likelihood-Free Inferencecited by 216
  10. 2017Flexible statistical inference for mechanistic models of neural dynamicscited by 162
  11. 2021Benchmarking Simulation-Based Inferencecited by 160
  12. 2018Neural Importance Samplingcited by 154
  13. 2020BayesFlow: Learning complex stochastic models with invertible neural networkscited by 139
  14. 2020On Contrastive Learning for Likelihood-free Inferencecited by 96
  15. 2015Approximating Likelihood Ratios with Calibrated Discriminative Classifierscited by 87
  16. 2016Likelihood-free inference by ratio estimationcited by 80
  17. 2021Real-time gravitational-wave science with neural posterior estimationcited by 76
  18. 2018Likelihood-free inference with emulator networkscited by 61
  19. 2022Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Modelscited by 50
  20. 2019Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomycited by 36
  21. 2022Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inferencecited by 28
  22. 2022Towards Reliable Simulation-Based Inference with Balanced Neural Ratio Estimationcited by 27
  23. 2020Complete parameter inference for GW150914 using deep learningcited by 25
  24. 2014High-Dimensional Density Ratio Estimation with Extensions to Approximate Likelihood Computationcited by 19
  25. 2020Gravitational-wave parameter estimation with autoregressive neural network flowscited by 19
  26. 2020Lightning-Fast Gravitational Wave Parameter Inference through Neural Amortizationcited by 17
  27. 2021Group equivariant neural posterior estimationcited by 16
  28. 2023Balancing Simulation-based Inference for Conservative Posteriorscited by 10
  29. 2019Likelihood-free MCMC with Amortized Approximate Ratio Estimatorscited by 9
  30. 2018Approximating the Likelihood in Approximate Bayesian Computationcited by 5
  31. 2022Adapting to noise distribution shifts in flow-based gravitational-wave inferencecited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 21; 2025: 42; 2026: 29.

97 papers.

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  1. 2024Variational Flow Matching for Graph Generationcited by 78
  2. 2024All-in-one simulation-based inferencecited by 71
  3. 2025Do-PFN: In-Context Learning for Causal Effect Estimationcited by 46
  4. 2024Conditional Wasserstein Distances with Applications in Bayesian OT Flow Matchingcited by 34
  5. 2025Simulation-Based Inference: A Practical Guidecited by 30
  6. 2024Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Predictioncited by 28
  7. 2023Free-form Flows: Make Any Architecture a Normalizing Flowcited by 26
  8. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 24
  9. 2024sbi reloaded: a toolkit for simulation-based inference workflowscited by 23
  10. 2023Consistency Models for Scalable and Fast Simulation-Based Inferencecited by 22
  11. 2024Real-time gravitational-wave inference for binary neutron stars using machine learningcited by 21
  12. 2025Position: The Future of Bayesian Prediction Is Prior-Fittedcited by 19
38 more
  1. 2025High-Order Matching for One-Step Shortcut Diffusion Modelscited by 15
  2. 2025Exponential Family Variational Flow Matching for Tabular Data Generationcited by 15
  3. 2024Reflected Flow Matchingcited by 13
  4. 2025Effortless, Simulation-Efficient Bayesian Inference using Tabular Foundation Modelscited by 13
  5. 2025Beyond Optimal Transport: Model-Aligned Coupling for Flow Matchingcited by 13
  6. 2024Amortized Bayesian Multilevel Modelscited by 12
  7. 2025Distribution Transformers: Fast Approximate Bayesian Inference With On-The-Fly Prior Adaptationcited by 12
  8. 2025Does Unsupervised Domain Adaptation Improve the Robustness of Amortized Bayesian Inference? A Systematic Evaluationcited by 10
  9. 2025Theoretical Guarantees for High Order Trajectory Refinement in Generative Flowscited by 9
  10. 2025Simulation-based Bayesian inference under model misspecificationcited by 9
  11. 2025Controlled Generation with Equivariant Variational Flow Matchingcited by 9
  12. 2025Multi-agent Coordination via Flow Matchingcited by 9
  13. 2023Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimationcited by 8
  14. 2024Compositional simulation-based inference for time seriescited by 8
  15. 2024FUSE: Fast Unified Simulation and Estimation for PDEscited by 6
  16. 2024Conditional diffusions for amortized neural posterior estimationcited by 6
  17. 2024A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference)cited by 5
  18. 2024Simulation-based Inference with the Python Package sbijaxcited by 5
  19. 2025Multilevel neural simulation-based inferencecited by 5
  20. 2025CP4SBI: Local Conformal Calibration of Credible Sets in Simulation-Based Inferencecited by 5
  21. 2025Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolantscited by 5
  22. 2023Inferring Atmospheric Properties of Exoplanets with Flow Matching and Neural Importance Samplingcited by 4
  23. 2024Simulation-Based Inference with Quantile Regressioncited by 4
  24. 2024Fast and Reliable Probabilistic Reflectometry Inversion with Prior-Amortized Neural Posterior Estimationcited by 4
  25. 2025CFMI: Flow Matching for Missing Data Imputationcited by 4
  26. 2025Purrception: Variational Flow Matching for Vector-Quantized Image Generationcited by 4
  27. 2026Zero-Flow Encoderscited by 4
  28. 2023Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inferencecited by 3
  29. 2024Amortized Bayesian Workflowcited by 3
  30. 2024Embed and Emulate: Contrastive representations for simulation-based inferencecited by 3
  31. 2025Amortized Bayesian Mixture Modelscited by 3
  32. 2025Posterior SBC: Simulation-Based Calibration Checking Conditional on Datacited by 3
  33. 2025FNOPE: Simulation-based inference on function spaces with Fourier Neural Operatorscited by 3
  34. 2025Conditional Flow Matching for Bayesian Posterior Inferencecited by 3
  35. 2025PriorGuide: Test-Time Prior Adaptation for Simulation-Based Inferencecited by 3
  36. 2026Tyche: One Step Flow for Efficient Probabilistic Weather Forecastingcited by 3
  37. 2024Flow Matching for Posterior Inference with Simulator Feedbackcited by 2
  38. 2025ConDiSim: Conditional Diffusion Models for Simulation Based Inferencecited by 2

50 most cited of 97 All 97 (JSON)

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  1. 2026GenSBI: Generative Methods for Simulation-Based Inference in JAX
  2. 2025Provable Mixed-Noise Learning with Flow-Matching
  3. 2024Flow Matching Posterior Sampling: A Training-free Conditional Generation for Flow Matching
  4. 2026D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching
  5. 2026Accelerated Sequential Flow Matching: A Bayesian Filtering Perspective
  6. 2025Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment
  7. 2025Fine-Tuning Flow Matching via Maximum Likelihood Estimation of Reconstructions
  8. 2024Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flows