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arxiv: 2605.27499 · v1 · pith:2RBUNTVXnew · submitted 2026-05-26 · 💻 cs.LG · astro-ph.CO· astro-ph.IM· physics.comp-ph· stat.ML

GenSBI: Generative Methods for Simulation-Based Inference in JAX

Aurelio Amerio This is my paper

Pith reviewed 2026-06-29 18:42 UTC · model grok-4.3

classification 💻 cs.LG astro-ph.COastro-ph.IMphysics.comp-phstat.ML
keywords simulation-based inferenceflow matchingscore matchingdenoising diffusionJAXgenerative modelstransformer architecturesposterior estimation
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The pith

GenSBI supplies a JAX library that runs flow matching, score matching, and denoising diffusion for simulation-based inference.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents GenSBI as an open-source library that brings three generative density-estimation methods to the JAX ecosystem for simulation-based inference. It supplies interchangeable transformer backbones and a unified interface that separates the choice of generative objective from the neural architecture and the inference task. Validation on standard SBIBM benchmarks yields C2ST scores between 0.50 and 0.56 together with well-calibrated posterior coverage. The library also supplies built-in calibration diagnostics and supports custom embedding networks for domain-specific models.

Core claim

GenSBI implements flow matching, score matching, and denoising diffusion entirely in JAX through three transformer architectures—SimFormer, Flux1, and the novel Flux1Joint—delivered via a single interface that decouples generative method, neural backbone, and inference mode, and reports near-ideal mean C2ST scores on SBIBM tasks with minimal per-task tuning.

What carries the argument

The unified interface that decouples generative method from neural backbone from inference mode, together with the gate-modulated transformer blocks extended to joint density estimation.

If this is right

  • JAX users can train and deploy generative SBI models without switching frameworks for the inference step.
  • The same code base supports posterior, likelihood, and joint-density estimation by swapping only the inference mode flag.
  • Custom domain-specific embedding networks can be dropped in without rewriting the generative training loop.
  • Built-in SBC, TARP, and LC2ST routines allow immediate checking of posterior calibration after training.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The availability of native JAX implementations may lower the barrier for teams whose forward simulators are already written in JAX or JAX-based autodiff ecosystems.
  • Because the architectures are interchangeable, the library could serve as a testbed for comparing how different transformer variants affect calibration across SBI tasks.
  • Extending the Flux1Joint block to additional modalities or higher-dimensional observations would be a direct next step permitted by the modular design.

Load-bearing premise

The JAX code produces the same numerical behavior and optimization targets as the original PyTorch reference implementations of flow matching, score matching, and denoising diffusion.

What would settle it

Running identical SBIBM tasks in both GenSBI and an established PyTorch SBI library and checking whether the C2ST scores and posterior-coverage diagnostics match within sampling noise.

Figures

Figures reproduced from arXiv: 2605.27499 by Aurelio Amerio.

Figure 1
Figure 1. Figure 1: The simulation-based inference pipeline. [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of the four neural density estimation strategies for simulation-based inference. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic of score-based generative modeling. The forward SDE progressively corrupts [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Unconditional density estimation with score matching (VE SDE) [ [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schematic of the EDM framework. The forward SDE is the same noise-corruption process [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Same as Figure 4, but using the EDM stochastic sampler [ [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Schematic of flow matching with the conditional optimal-transport (CondOT) path. The top [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Same as Figures 4 and 6, but using flow matching with the conditional optimal-transport [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of individual sample trajectories during unconditional density estimation on [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: GenSBI’s three-axis architecture. Generative methods (left) inject into pipelines (centre) [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Training and inference workflows. During training (top), the generative method prepares [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: The model wrapper adapter pattern. Each wrapper translates the pipeline’s unified calling [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: SimFormer architecture. Each scalar component of the joint vector [PITH_FULL_IMAGE:figures/full_fig_p028_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Flux1 architecture. Two separate token streams — an observation stream (noisy parameters [PITH_FULL_IMAGE:figures/full_fig_p030_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Flux1Joint architecture. Like SimFormer, the model processes a single joint token [PITH_FULL_IMAGE:figures/full_fig_p031_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: Marginal posterior distributions for the Two Moons task (Flux1Joint, flow matching, [PITH_FULL_IMAGE:figures/full_fig_p041_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Best C2ST accuracy as a function of simulation budget for the Flux1 architecture across [PITH_FULL_IMAGE:figures/full_fig_p042_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Best C2ST accuracy as a function of simulation budget for the Flux1Joint architecture [PITH_FULL_IMAGE:figures/full_fig_p042_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: C2ST accuracy as a function of simulation budget, comparing the best GenSBI model [PITH_FULL_IMAGE:figures/full_fig_p043_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: TARP expected coverage probability curve for the Two Moons task (Flux1Joint, flow [PITH_FULL_IMAGE:figures/full_fig_p043_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Gravitational wave parameter estimation task (Flux1, flow matching, EMA). [PITH_FULL_IMAGE:figures/full_fig_p044_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: TARP expected coverage probability curve for the gravitational wave task (Flux1, flow [PITH_FULL_IMAGE:figures/full_fig_p045_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Strong gravitational lensing task (Flux1, flow matching, EMA). [PITH_FULL_IMAGE:figures/full_fig_p045_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: TARP expected coverage probability curve for the strong lensing task (Flux1, flow [PITH_FULL_IMAGE:figures/full_fig_p046_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Marginal posterior distributions for the Gaussian Linear task (Flux1Joint, flow matching, [PITH_FULL_IMAGE:figures/full_fig_p054_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: TARP expected coverage probability curve for the Gaussian Linear task. [PITH_FULL_IMAGE:figures/full_fig_p055_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Marginal posterior distributions for the Gaussian Mixture task (Flux1Joint, flow matching, [PITH_FULL_IMAGE:figures/full_fig_p055_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: TARP expected coverage probability curve for the Gaussian Mixture task. [PITH_FULL_IMAGE:figures/full_fig_p056_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Marginal posterior distributions for the SLCP task (Flux1Joint, flow matching, EMA). [PITH_FULL_IMAGE:figures/full_fig_p057_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: TARP expected coverage probability curve for the SLCP task. [PITH_FULL_IMAGE:figures/full_fig_p057_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: Marginal posterior distributions for the Bernoulli GLM task (Flux1Joint, flow matching, [PITH_FULL_IMAGE:figures/full_fig_p058_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: TARP expected coverage probability curve for the Bernoulli GLM task. [PITH_FULL_IMAGE:figures/full_fig_p058_33.png] view at source ↗
read the original abstract

Flow and diffusion generative models have established themselves as widely adopted density estimators for simulation-based inference (SBI), extending naturally from neural posterior estimation to likelihood and joint density estimation. Their principled optimization objectives and freedom from architectural constraints have driven rapid adoption across the natural sciences. Yet the most widely used SBI libraries remain PyTorch-based, leaving researchers who develop their forward models and analysis pipelines in JAX without a native option. We present GenSBI, an open-source library that implements flow matching, score matching, and denoising diffusion entirely in JAX. The library offers three transformer-based architectures - SimFormer, Flux1, and a novel Flux1Joint that extends gate-modulated transformer blocks to joint density estimation - all interchangeable through a unified interface that decouples generative method, neural backbone, and inference mode. GenSBI provides an end-to-end workflow from training through posterior calibration (SBC, TARP, LC2ST) and supports custom architectures with domain-specific embedding networks. We validate the framework on standard SBI benchmarks, achieving near-ideal mean C2ST scores (0.50-0.56, where 0.50 is ideal) on SBIBM tasks with minimal per-task tuning and well-calibrated posterior coverage across all tested configurations. The code is publicly available at https://github.com/aurelio-amerio/GenSBI.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript presents GenSBI, an open-source JAX library implementing flow matching, score matching, and denoising diffusion for simulation-based inference. It introduces three interchangeable transformer backbones (SimFormer, Flux1, Flux1Joint) with a unified interface, supports custom embeddings, and provides end-to-end workflows including posterior calibration diagnostics. Validation on SBIBM tasks reports near-ideal mean C2ST scores (0.50-0.56) with minimal per-task tuning and well-calibrated coverage.

Significance. If the implementations are correct, the library fills a clear gap by providing native JAX support for generative SBI methods, allowing seamless use with JAX-based simulators. The modular design decoupling method, backbone, and inference mode, plus explicit support for SBC/TARP/LC2ST calibration, represents a practical contribution. The reported benchmark performance, if verified, would demonstrate utility with limited tuning.

major comments (1)
  1. [Experiments] Experiments section (and abstract performance claims): The reported C2ST scores (0.50-0.56) and calibration metrics are presented as evidence of correct implementation, yet no explicit verification is described (e.g., loss-value matching, gradient agreement, or sampling-distribution equivalence tests) against established PyTorch reference implementations of flow/score matching and diffusion. This verification is load-bearing for the central claim that the JAX code faithfully realizes the intended generative objectives.
minor comments (2)
  1. The abstract and §3 could clarify the precise SBIBM task suite and version used, as well as the hyperparameter search ranges that support the 'minimal per-task tuning' claim.
  2. [§3] Notation for the Flux1Joint architecture (gate-modulated blocks for joint density) should be defined explicitly in §3 before use in experiments.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for highlighting the importance of implementation verification. We address the single major comment below and will revise the manuscript to strengthen this aspect.

read point-by-point responses

  1. Referee: [Experiments] Experiments section (and abstract performance claims): The reported C2ST scores (0.50-0.56) and calibration metrics are presented as evidence of correct implementation, yet no explicit verification is described (e.g., loss-value matching, gradient agreement, or sampling-distribution equivalence tests) against established PyTorch reference implementations of flow/score matching and diffusion. This verification is load-bearing for the central claim that the JAX code faithfully realizes the intended generative objectives.

    Authors: We agree that explicit cross-framework verification would provide stronger evidence for faithful implementation of the generative objectives. The current validation demonstrates that the reported C2ST scores (0.50-0.56) and calibration metrics match the expected near-ideal performance on SBIBM tasks, which would be improbable under significant implementation deviations. However, we acknowledge the referee's point that this constitutes indirect rather than direct evidence. In the revised manuscript we will add a dedicated subsection under Experiments that reports (i) training-loss agreement on shared tasks with available PyTorch references, (ii) gradient-norm comparisons where architectures permit, and (iii) distributional equivalence checks via Kolmogorov-Smirnov tests on posterior samples for at least the flow-matching and score-matching backbones. For denoising diffusion we will note the absence of a directly comparable open-source PyTorch SBI reference and rely on the calibration diagnostics already presented. revision: yes

Circularity Check

0 steps flagged

No circularity: performance metrics drawn from external SBIBM benchmarks, not self-defined quantities

full rationale

The paper describes a JAX library implementing established methods (flow matching, score matching, denoising diffusion) with transformer backbones and reports C2ST scores and calibration on SBIBM tasks. These benchmarks are independent external standards; the results are not predictions derived from the library's own fitted parameters or reduced by self-citation chains. No load-bearing self-definitional steps, fitted-input predictions, or ansatz smuggling appear in the abstract or described claims. The central validation rests on external data rather than internal redefinitions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the correctness of the JAX implementations of established generative objectives and on the representativeness of the SBIBM benchmark suite; no free parameters, axioms, or invented physical entities are introduced beyond standard neural-network hyperparameters.

pith-pipeline@v0.9.1-grok · 5781 in / 1095 out tokens · 18688 ms · 2026-06-29T18:42:11.067699+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

84 extracted references · 59 canonical work pages · 28 internal anchors

  1. [1]

    First results from the IllustrisTNG simulations: matter and galaxy clustering

    V . Springel, R. Pakmor, A. Pillepich, R. Weinberger, D. Nelson, L. Hernquist et al.,First results from the IllustrisTNG simulations: matter and galaxy clustering,Monthly Notices of the Royal Astronomical Society475(2017) 676 [1707.03397]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  2. [2]

    Villaescusa-Navarro, D

    F. Villaescusa-Navarro, D. Anglés-Alcázar, S. Genel, D.N. Spergel, R.S. Somerville, R. Dave et al.,The CAMELS Project: Cosmology and Astrophysics with Machine-learning Simulations, The Astrophysical Journal915(2021) 71 [2010.00619]

    work page arXiv 2021

  3. [3]

    Cranmer, J

    K. Cranmer, J. Brehmer and G. Louppe,The frontier of simulation-based inference, Proceedings of the National Academy of Sciences117(2020) 30055 [1911.01429]

    work page arXiv 2020

  4. [4]

    M. Dax, J. Wildberger, S. Buchholz, S.R. Green, J.H. Macke and B. Schölkopf,Flow Matching for Scalable Simulation-Based Inference,2305.17161

    work page arXiv

  5. [5]

    Dax, S.R

    M. Dax, S.R. Green, J. Gair, J.H. Macke, A. Buonanno and B. Schölkopf,Real-Time Gravitational Wave Science with Neural Posterior Estimation,Phys. Rev. Lett.127(2021) 241103 [2106.12594]

    work page arXiv 2021

  6. [6]

    Carr, M.J

    M.J. Carr, M.J. Simpson and C. Drovandi,Estimating parameters of a stochastic cell invasion model with fluorescent cell cycle labelling using approximate Bayesian computation,J. R. Soc. Interface18(2021) 20210362

    2021

  7. [7]

    Wang, R.P

    X. Wang, R.P. Kelly, A.L. Jenner, D.J. Warne and C. Drovandi,A Comprehensive Guide to Simulation-based Inference in Computational Biology,2409.19675

    work page arXiv

  8. [8]

    Rodrigues, T

    P.L.C. Rodrigues, T. Moreau, G. Louppe and A. Gramfort,HNPE: Leveraging Global Parameters for Neural Posterior Estimation,2102.06477

    work page arXiv

  9. [9]

    Hashemi, A.N

    M. Hashemi, A.N. Vattikonda, J. Jha, V . Sip, M.M. Woodman, F. Bartolomei et al.,Amortized Bayesian inference on generative dynamical network models of epilepsy using deep neural density estimators,Neural Networks163(2023) 178

    2023

  10. [10]

    Radev, F

    S.T. Radev, F. Graw, S. Chen, N.T. Mutters, V .M. Eichel, T. Bärnighausen et al.,OutbreakFlow: Model-based Bayesian inference of disease outbreak dynamics with invertible neural networks and its application to the COVID-19 pandemics in Germany,PLOS Comput. Biol.17(2021) e1009472 [2010.00300]

    work page arXiv 2021

  11. [11]

    Metropolis, A.W

    N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller,Equation of state calculations by fast computing machines,The Journal of Chemical Physics21(1953) 1087

    1953

  12. [12]

    Hastings,Monte Carlo Sampling Methods Using Markov Chains and Their Applications, Biometrika57(1970) 97

    W.K. Hastings,Monte Carlo Sampling Methods Using Markov Chains and Their Applications, Biometrika57(1970) 97

    1970

  13. [13]

    Duane, A.D

    S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth,Hybrid Monte Carlo,Physics Letters. B. Particle Physics, Nuclear Physics and Cosmology195(1987) 216

    1987

  14. [14]

    Microcanonical Hamiltonian Monte Carlo

    J. Robnik, G.B. De Luca, E. Silverstein and U. Seljak,Microcanonical Hamiltonian Monte Carlo,2212.08549

    work page internal anchor Pith review Pith/arXiv arXiv

  15. [15]

    Skilling,Nested sampling for general Bayesian computation,Bayesian Analysis1(2006) 833

    J. Skilling,Nested sampling for general Bayesian computation,Bayesian Analysis1(2006) 833. 48

    2006

  16. [16]

    Sisson, Y

    S.A. Sisson, Y . Fan and M.A. Beaumont,Overview of Approximate Bayesian Computation,

  17. [17]

    10.1201/9781315117195-1

    work page doi:10.1201/9781315117195-1

  18. [18]

    Wood,Statistical inference for noisy nonlinear ecological dynamic systems,Nature466 (2010) 1102

    S.N. Wood,Statistical inference for noisy nonlinear ecological dynamic systems,Nature466 (2010) 1102

    2010

  19. [19]

    Automatic Posterior Transformation for Likelihood-Free Inference

    D.S. Greenberg, M. Nonnenmacher and J.H. Macke,Automatic Posterior Transformation for Likelihood-Free Inference, inInternational Conference on Machine Learning, 2019, DOI [1905.07488]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  20. [20]

    Radev, U.K

    S.T. Radev, U.K. Mertens, A. V oss, L. Ardizzone and U. Köthe,BayesFlow: Learning complex stochastic models with invertible neural networks, inIEEE Transactions on Neural Networks and Learning Systems, 2020, DOI [2003.06281]

    work page arXiv 2020

  21. [21]

    Fast $\epsilon$-free Inference of Simulation Models with Bayesian Conditional Density Estimation

    G. Papamakarios and I. Murray,Fastϵ-free Inference of Simulation Models with Bayesian Conditional Density Estimation, inAdvances in Neural Information Processing Systems, vol. 29, 2016, DOI [1605.06376]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  22. [22]

    Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows

    G. Papamakarios, D.C. Sterratt and I. Murray,Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flows,1805.07226

    work page internal anchor Pith review Pith/arXiv arXiv

  23. [23]

    Deistler, J

    M. Deistler, J. Boelts, P. Steinbach, G. Moss, T. Moreau, M. Gloeckler et al.,Simulation-Based Inference: A Practical Guide,2508.12939

    work page arXiv

  24. [24]

    Hermans, V

    J. Hermans, V . Begy and G. Louppe,Likelihood-free MCMC with Amortized Approximate Ratio Estimators,1903.04057

    work page arXiv 1903

  25. [25]

    B. Uria, I. Murray and H. Larochelle,RNADE: The real-valued neural autoregressive density-estimator,Advances in Neural Information Processing Systems26(2013) [1306.0186]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  26. [26]

    Neural Autoregressive Distribution Estimation

    B. Uria, M.-A. Côté, K. Gregor, I. Murray and H. Larochelle,Neural autoregressive distribution estimation,Journal of Machine Learning Research17(2016) 1 [1605.02226]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  27. [27]

    Gloeckler, M

    M. Gloeckler, M. Deistler and J.H. Macke,All-in-one simulation-based inference, in International Conference on Machine Learning, 2024, DOI [2404.09636]

    work page arXiv 2024

  28. [28]

    Lueckmann, J

    J.-M. Lueckmann, J. Boelts, D.S. Greenberg, P.J. Gonçalves and J.H. Macke,Benchmarking Simulation-Based Inference, inInternational Conference on Artificial Intelligence and Statistics, 2021, DOI [2101.04653]

    work page arXiv 2021

  29. [29]

    Boelts, M

    J. Boelts, M. Deistler, M. Gloeckler, Álvaro Tejero-Cantero, J.-M. Lueckmann, G. Moss et al., sbi reloaded: a toolkit for simulation-based inference workflows,Journal of Open Source Software10(2025) 7754

    2025

  30. [30]

    PyTorch: An Imperative Style, High-Performance Deep Learning Library

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan et al.,PyTorch: An Imperative Style, High-Performance Deep Learning Library, inAdvances in Neural Information Processing Systems, vol. 32, 2019, DOI [1912.01703]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  31. [31]

    Miller, A

    B.K. Miller, A. Cole, C. Weniger, F. Nattino, O. Ku and M.W. Grootes,swyft: Truncated Marginal Neural Ratio Estimation in Python,Journal of Open Source Software7(2022) 4205

    2022

  32. [32]

    TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis

    Y . Lipman, R.T.Q. Chen, H. Ben-Hamu, M. Nickel and M. Le,Flow Matching for Generative Modeling, inInternational Conference on Learning Representations, 2023, DOI [2210.02186]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  33. [33]

    Y . Song, J. Sohl-Dickstein, D.P. Kingma, A. Kumar, S. Ermon and B. Poole,Score-Based Generative Modeling through Stochastic Differential Equations,2011.13456

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  34. [34]

    Elucidating the Design Space of Diffusion-Based Generative Models

    T. Karras, M. Aittala, T. Aila and S. Laine,Elucidating the Design Space of Diffusion-Based Generative Models,Advances in Neural Information Processing Systems 3535(2022) 26565 [2206.00364]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  35. [35]

    L. Wang, C. Song, Z. Liu, Y . Rong, Q. Liu, S. Wu et al.,Diffusion Models for Molecules: A Survey of Methods and Tasks,2502.09511

    work page arXiv

  36. [36]

    Dingeldein, P

    L. Dingeldein, P. Cossio and R. Covino,Simulation-based inference of single-molecule experiments,Current Opinion in Structural Biology91(2025) 102988

    2025

  37. [37]

    L. Yang, Z. Zhang, Y . Song, S. Hong, R. Xu, Y . Zhao et al.,Diffusion Models: A Comprehensive Survey of Methods and Applications,2209.00796. 49

    work page arXiv

  38. [38]

    Arruda, N

    J. Arruda, N. Bracher, U. Köthe, J. Hasenauer and S.T. Radev,Diffusion Models in Simulation-Based Inference: A Tutorial Review,2512.20685

    work page arXiv

  39. [39]

    Nautiyal, L

    M. Nautiyal, L. Ju, M. Ernfors, K. Hagland, V . Holma, M. Werkö Söderholm et al., OneFlowSBI: One Model, Many Queries for Simulation-Based Inference,2601.22951

    work page arXiv

  40. [40]

    JAX: composable transformations of Python+NumPy programs

    J. Bradbury, R. Frostig, P. Hawkins, M.J. Johnson, C. Leary, D. Maclaurin et al., “JAX: composable transformations of Python+NumPy programs.” http://github.com/jax-ml/jax, 2018

    2018

  41. [41]

    Cabezas, A

    A. Cabezas, A. Corenflos, J. Lao and R. Louf,BlackJAX: Composable Bayesian inference in JAX,2402.10797

    work page arXiv

  42. [42]

    D. Phan, N. Pradhan and M. Jankowiak,Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro,1912.11554

    work page internal anchor Pith review Pith/arXiv arXiv 1912

  43. [43]

    Dirmeier, S

    S. Dirmeier, S. Ulzega, A. Mira and C. Albert,Simulation-based inference with the Python package sbijax,2409.19435

    work page arXiv

  44. [44]

    Flax: A neural network library and ecosystem for JAX

    J. Heek, A. Levskaya, A. Oliver, M. Ritter, B. Rondepierre, A. Steiner et al., “Flax: A neural network library and ecosystem for JAX.”http://github.com/google/flax, 2024

    2024

  45. [45]

    FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space

    Black Forest Labs, S. Batifol, A. Blattmann, F. Boesel, S. Consul, C. Diagne et al.,FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space, 2506.15742

    work page internal anchor Pith review Pith/arXiv arXiv

  46. [46]

    Diggle and R.J

    P.J. Diggle and R.J. Gratton,Monte Carlo Methods of Inference for Implicit Statistical Models, Journal of the Royal Statistical Society: Series B (Methodological)46(1984) 193

    1984

  47. [47]

    High-Resolution Image Synthesis with Latent Diffusion Models

    R. Rombach, A. Blattmann, D. Lorenz, P. Esser and B. Ommer,High-Resolution Image Synthesis with Latent Diffusion Models, inIEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022, DOI [2112.10752]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  48. [48]

    Boelts, J.-M

    J. Boelts, J.-M. Lueckmann, R. Gao and J.H. Macke,Flexible and efficient simulation-based inference for models of decision-making,eLife11(2022) e77220

    2022

  49. [49]

    X. Ai, Y . He, A. Gu, R. Salakhutdinov, J.Z. Kolter, N.M. Boffi et al.,Joint Distillation for Fast Likelihood Evaluation and Sampling in Flow-based Models,2512.02636

    work page internal anchor Pith review Pith/arXiv arXiv

  50. [50]

    Scheutwinkel, W

    K.H. Scheutwinkel, W. Handley, C. Weniger and E. de Lera Acedo,PolySwyft: sequential simulation-based nested sampling,2512.08316

    work page arXiv

  51. [51]

    Masked Autoregressive Flow for Density Estimation

    G. Papamakarios, T. Pavlakou and I. Murray,Masked Autoregressive Flow for Density Estimation,1705.07057

    work page internal anchor Pith review Pith/arXiv arXiv

  52. [52]

    Durkan, A

    C. Durkan, A. Bekasov, I. Murray and G. Papamakarios,Neural Spline Flows, inAdvances in Neural Information Processing Systems, vol. 32, 2019, DOI [1906.04032]

    work page arXiv 2019

  53. [53]

    Flow Matching Guide and Code

    Y . Lipman, M. Havasi, P. Holderrieth, N. Shaul, M. Le, B. Karrer et al.,Flow Matching Guide and Code,2412.06264

    work page internal anchor Pith review Pith/arXiv arXiv

  54. [54]

    Stochastic Interpolants: A Unifying Framework for Flows and Diffusions

    M.S. Albergo, N.M. Boffi and E. Vanden-Eijnden,Stochastic Interpolants: A Unifying Framework for Flows and Diffusions,2303.08797

    work page internal anchor Pith review Pith/arXiv arXiv

  55. [55]

    Zammit-Mangion, M

    A. Zammit-Mangion, M. Sainsbury-Dale and R. Huser,Neural methods for amortized inference,Annual Review of Statistics and Its Application12(2025) 311 [2404.12484]

    work page arXiv 2025

  56. [56]

    Deep Unsupervised Learning using Nonequilibrium Thermodynamics

    J. Sohl-Dickstein, E.A. Weiss, N. Maheswaranathan and S. Ganguli,Deep Unsupervised Learning using Nonequilibrium Thermodynamics,1503.03585

    work page internal anchor Pith review Pith/arXiv arXiv

  57. [57]

    J. Ho, A. Jain and P. Abbeel,Denoising Diffusion Probabilistic Models,2006.11239

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  58. [58]

    Generative Modeling by Estimating Gradients of the Data Distribution

    Y . Song and S. Ermon,Generative Modeling by Estimating Gradients of the Data Distribution, inAdvances in Neural Information Processing Systems, vol. 32, 2019, DOI [1907.05600]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  59. [59]

    Song and S

    Y . Song and S. Ermon,Improved Techniques for Training Score-Based Generative Models, in Advances in Neural Information Processing Systems, vol. 33, 2020, DOI [2006.09011]

    work page arXiv 2020

  60. [60]

    Hyvärinen, J

    A. Hyvärinen, J. Hurri and P.O. Hoyer,Estimation of Non-Normalized Statistical Models by Score Matching,Journal of Machine Learning Research6(2005) 695

    2005

  61. [61]

    Vincent,A connection between score matching and denoising autoencoders,Neural Computation23(2011) 1661

    P. Vincent,A connection between score matching and denoising autoencoders,Neural Computation23(2011) 1661. 50

    2011

  62. [62]

    Anderson,Reverse-time diffusion equation models,Stochastic Processes and their Applications12(1982) 313

    B.D.O. Anderson,Reverse-time diffusion equation models,Stochastic Processes and their Applications12(1982) 313

    1982

  63. [63]

    Kidger,On Neural Differential Equations, Ph.D

    P. Kidger,On Neural Differential Equations, Ph.D. thesis, University of Oxford, 2021

    2021

  64. [64]

    A. Tong, K. Fatras, N. Malkin, G. Huguet, Y . Zhang, J. Rector-Brooks et al.,Improving and Generalizing Flow-Based Generative Models with Minibatch Optimal Transport, 2302.00482

    work page internal anchor Pith review Pith/arXiv arXiv

  65. [65]

    Cheng and A

    H.K. Cheng and A. Schwing,The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generation,2503.10636

    work page arXiv

  66. [66]

    X. Liu, C. Gong and Q. Liu,Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow,2209.03003

    work page internal anchor Pith review Pith/arXiv arXiv

  67. [67]

    Singh and I

    S. Singh and I. Fischer,Stochastic Sampling from Deterministic Flow Models,2410.02217

    work page arXiv

  68. [68]

    Scalable Diffusion Models with Transformers

    W. Peebles and S. Xie,Scalable Diffusion Models with Transformers, inIEEE/CVF International Conference on Computer Vision, 2023, DOI [2212.09748]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  69. [69]

    An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

    A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Unterthiner et al.,An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale,2010.11929

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  70. [70]

    GenSBI-examples: Benchmark examples for GenSBI

    A. Amerio, “GenSBI-examples: Benchmark examples for GenSBI.” https://github.com/aurelio-amerio/GenSBI-examples, 2025

    2025

  71. [71]

    Hutchinson,A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines,Communications in Statistics – Simulation and Computation18(1989) 1059

    M.F. Hutchinson,A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian Smoothing Splines,Communications in Statistics – Simulation and Computation18(1989) 1059

    1989

  72. [72]

    1804.06788 , archivePrefix =

    S. Talts, M. Betancourt, D. Simpson, A. Vehtari and A. Gelman,Validating Bayesian Inference Algorithms with Simulation-Based Calibration,1804.06788

    work page arXiv

  73. [73]

    Lemos, A

    P. Lemos, A. Coogan, Y . Hezaveh and L. Perreault-Levasseur,Sampling-Based Accuracy Testing of Posterior Estimators for General Inference, inInternational Conference on Machine Learning, 2023, DOI [2302.03026]

    work page arXiv 2023

  74. [74]

    Linhart, A

    J. Linhart, A. Gramfort and P.L.C. Rodrigues,L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference, inAdvances in Neural Information Processing Systems, vol. 36, 2023, DOI [2306.03580]

    work page arXiv 2023

  75. [75]

    Orbax: Training checkpointing and persistence utilities for JAX

    Google DeepMind, “Orbax: Training checkpointing and persistence utilities for JAX.” https://github.com/google/orbax, 2024

    2024

  76. [76]

    A. Nitz, I. Harry, D. Brown, C.M. Biwer, J. Willis, T.D. Canton et al., “Pycbc.” https://github.com/gwastro/pycbc, 2024. 10.5281/zenodo.10473621

    work page doi:10.5281/zenodo.10473621 2024

  77. [77]

    Christensen and R

    N. Christensen and R. Meyer,Parameter estimation with gravitational waves,Reviews of Modern Physics94(2022) 025001 [2204.04449]

    work page arXiv 2022

  78. [78]

    Strong Lensing by Galaxies

    T. Treu,Strong Lensing by Galaxies,Annual Review of Astronomy and Astrophysics48(2010) 87 [1003.5567]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  79. [79]

    Z. Geng, M. Deng, X. Bai, J.Z. Kolter and K. He,Mean Flows for One-step Generative Modeling,2505.13447

    work page internal anchor Pith review Pith/arXiv arXiv

  80. [80]

    Revisiting Classifier Two-Sample Tests

    D. Lopez-Paz and M. Oquab,Revisiting Classifier Two-Sample Tests,1610.06545

    work page internal anchor Pith review Pith/arXiv arXiv

Showing first 80 references.