mlsanityData to 7 Oct 2026

Sequential Neural Score Estimation: Likelihood-Free Inference with Conditional Score Based Diffusion Models

arXiv 2210.04872 ↗First posted 10 Oct 2022stat.ML cs.LGcited by 50

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

We introduce Sequential Neural Posterior Score Estimation (SNPSE), a score-based method for Bayesian inference in simulator-based models. Our method, inspired by the remarkable success of score-based methods in generative modelling, leverages conditional score-based diffusion models to generate samples from the posterior distribution of interest. The model is trained using an objective function which directly estimates the score of the posterior. We embed the model into a sequential training procedure, which guides simulations using the current approximation of the posterior at the observation of interest, thereby reducing the simulation cost. We also introduce several alternative sequential approaches, and discuss their relative merits. We then validate our method, as well as its amortised, non-sequential, variant on several numerical examples, demonstrating comparable or superior performance to existing state-of-the-art methods such as Sequential Neural Posterior Estimation (SNPE).

Key facts. Cited by 50 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 82 of its 172 references that are in the map. First posted on arXiv 10 Oct 2022.

Builds on

82 of 172 references.

Closest ancestors · 17

Same direction, newest first

  1. 2022Classifier-Free Diffusion Guidance26 Jul
  2. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models10 Jun
  3. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  4. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  5. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  6. 2022Conditional Simulation Using Diffusion Schr"odinger Bridges27 Feb
  7. 2022Riemannian Score-Based Generative Modelling6 Feb
  8. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  9. 2021Conditional Image Generation with Score-Based Diffusion Models26 Nov
  10. 2021ILVR: Conditioning Method for Denoising Diffusion Probabilistic Models6 Aug
  11. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  12. 2021Cascaded Diffusion Models for High Fidelity Image Generation30 May
5 more
  1. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  2. 2021Maximum Likelihood Training of Score-Based Diffusion Models22 Jan
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  4. 2020Denoising Diffusion Probabilistic Models19 Jun
  5. 2020Improved Techniques for Training Score-Based Generative Models16 Jun

Other references · 65

  1. 2017Attention Is All You Needcited by 59,932
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2022Flow Matching for Generative Modelingcited by 5,426
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2018Neural Ordinary Differential Equationscited by 3,733
  7. 2016Improved Techniques for Training GANscited by 2,938
  8. 2022Video Diffusion Modelscited by 2,280
  9. 2015Variational Inference with Normalizing Flowscited by 2,161
  10. 2016Density estimation using Real NVPcited by 2,029
  11. 2016Variational Inference: A Review for Statisticianscited by 1,466
  12. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
38 more
  1. 2020DiffWave: A Versatile Diffusion Model for Audio Synthesiscited by 1,339
  2. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,315
  3. 2017Masked Autoregressive Flow for Density Estimationcited by 680
  4. 2020WaveGrad: Estimating Gradients for Waveform Generationcited by 620
  5. 2019Neural Spline Flowscited by 590
  6. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  7. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 577
  8. 2021Solving Inverse Problems in Medical Imaging with Score-Based Generative Modelscited by 514
  9. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  10. 2019The frontier of simulation-based inferencecited by 490
  11. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 445
  12. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  13. 2021Score-based diffusion models for accelerated MRIcited by 308
  14. 2021Robust Compressed Sensing MRI with Deep Generative Priorscited by 284
  15. 2016Revisiting Classifier Two-Sample Testscited by 258
  16. 2020Learning Gradient Fields for Shape Generationcited by 245
  17. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  18. 2020How to train your neural ODE: the world of Jacobian and kinetic regularizationcited by 228
  19. 2018Sequential Neural Likelihood: Fast Likelihood-free Inference with Autoregressive Flowscited by 217
  20. 2019Automatic Posterior Transformation for Likelihood-Free Inferencecited by 216
  21. 2016Unrolled Generative Adversarial Networkscited by 208
  22. 2017A Conceptual Introduction to Hamiltonian Monte Carlocited by 207
  23. 2017Flexible statistical inference for mechanistic models of neural dynamicscited by 162
  24. 2021Benchmarking Simulation-Based Inferencecited by 160
  25. 2021Symbolic Music Generation with Diffusion Modelscited by 152
  26. 2020On Contrastive Learning for Likelihood-free Inferencecited by 96
  27. 2015Approximating Likelihood Ratios with Calibrated Discriminative Classifierscited by 87
  28. 2016Likelihood-free inference by ratio estimationcited by 80
  29. 2018Likelihood-free inference with emulator networkscited by 61
  30. 2020A Non-Asymptotic Analysis for Stein Variational Gradient Descentcited by 61
  31. 2016Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimationcited by 50
  32. 2022Compositional Score Modeling for Simulation-based Inferencecited by 46
  33. 2022Denoising Likelihood Score Matching for Conditional Score-based Data Generationcited by 45
  34. 2018Stein Pointscited by 43
  35. 2022Variational methods for simulation-based inferencecited by 43
  36. 2022GATSBI: Generative Adversarial Training for Simulation-Based Inferencecited by 36
  37. 2019MadMiner: Machine learning-based inference for particle physicscited by 32
  38. 2021Sequential Neural Posterior and Likelihood Approximationcited by 30

50 most cited of 65 All 65 (JSON)

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 11; 2024: 12; 2025: 19; 2026: 8.

50 papers.

Sort:

By area:

  1. 2025PaperBench: Evaluating AI's Ability to Replicate AI Researchcited by 286
  2. 2023Flow Matching for Scalable Simulation-Based Inferencecited by 97
  3. 2024All-in-one simulation-based inferencecited by 71
  4. 2023Learning Robust Statistics for Simulation-based Inference under Model Misspecificationcited by 48
  5. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 24
  6. 2024sbi reloaded: a toolkit for simulation-based inference workflowscited by 23
  7. 2023Consistency Models for Scalable and Fast Simulation-Based Inferencecited by 22
  8. 2024Diffusion posterior sampling for simulation-based inference in tall data settingscited by 17
  9. 2023Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inferencecited by 14
  10. 2025Effortless, Simulation-Efficient Bayesian Inference using Tabular Foundation Modelscited by 13
  11. 2024Amortized Bayesian Multilevel Modelscited by 12
  12. 2025Distribution Transformers: Fast Approximate Bayesian Inference With On-The-Fly Prior Adaptationcited by 12
38 more
  1. 2023Balancing Simulation-based Inference for Conservative Posteriorscited by 10
  2. 2023Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probabilitycited by 10
  3. 2025Simulation-based Bayesian inference under model misspecificationcited by 9
  4. 2023Misspecification-robust Sequential Neural Likelihood for Simulation-based Inferencecited by 8
  5. 2023Simulation-based Inference for High-dimensional Data using Surjective Sequential Neural Likelihood Estimationcited by 8
  6. 2024Compositional simulation-based inference for time seriescited by 8
  7. 2024Conditional diffusions for amortized neural posterior estimationcited by 6
  8. 2024Simulation-based Inference with the Python Package sbijaxcited by 5
  9. 2025Multilevel neural simulation-based inferencecited by 5
  10. 2026Zero-Flow Encoderscited by 4
  11. 2023Simulation-based Inference with the Generalized Kullback-Leibler Divergencecited by 3
  12. 2023Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inferencecited by 3
  13. 2024Amortized Bayesian Workflowcited by 3
  14. 2025Amortized Bayesian Mixture Modelscited by 3
  15. 2025Posterior SBC: Simulation-Based Calibration Checking Conditional on Datacited by 3
  16. 2025PriorGuide: Test-Time Prior Adaptation for Simulation-Based Inferencecited by 3
  17. 2024Flow Matching for Posterior Inference with Simulator Feedbackcited by 2
  18. 2025JADAI: Jointly Amortizing Adaptive Design and Bayesian Inferencecited by 2
  19. 2023Approximate Stein Classes for Truncated Density Estimationcited by 1
  20. 2024Tree Bandits for Generative Bayescited by 1
  21. 2025Synthesizing 3D Abstractions by Inverting Procedural Buildings with Transformerscited by 1
  22. 2025Diffusion Models for Inverse Problems in the Exponential Familycited by 1
  23. 2025Neural Fidelity Calibration for Informative Sim-to-Real Adaptationcited by 1
  24. 2025Causal Posterior Estimationcited by 1
  25. 2025Trustworthy scientific inference with generative modelscited by 1
  26. 2025Error analysis of a compositional score-based algorithm for simulation-based inferencecited by 1
  27. 2025A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarioscited by 1
  28. 2026Amortized Simulation-Based Inference in Generalized Bayes via Neural Posterior Estimationcited by 1
  29. 2026An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learningcited by 1
  30. 2024Leveraging Nested MLMC for Sequential Neural Posterior Estimation with Intractable Likelihoodscited by 0
  31. 2025Direct Fisher Score Estimation for Likelihood Maximizationcited by 0
  32. 2025Fisher-Bingham-like normalizing flows on the spherecited by 0
  33. 2025A Black-Box Debiasing Framework for Conditional Samplingcited by 0
  34. 2026Theoretical guidelines for annealed Langevin dynamics in compositional simulation-based inferencecited by 0
  35. 2026Amortized Factor Inference Networks for Posterior Inferencecited by 0
  36. 2026MA-SBI: Misspecification-Aware Simulation-Based Inference via Side-Channel Guidancecited by 0
  37. 2026Guidance for Prior Change via Density Ratio Estimationcited by 0
  38. 2026Neural composite likelihood estimation: simulation based inference for time seriescited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Zero-Shot Conditioning of Score-Based Diffusion Models by Neuro-Symbolic Constraints
  2. 2024Nearest Neighbour Score Estimators for Diffusion Generative Models
  3. 2022Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching
  4. 2024Operator-Informed Score Matching for Markov Diffusion Models
  5. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
  6. 2023Score-based Diffusion Models for Bayesian Image Reconstruction
  7. 2022FP-Diffusion: Improving Score-based Diffusion Models by Enforcing the Underlying Score Fokker-Planck Equation
  8. 2023Closing the ODE-SDE gap in score-based diffusion models through the Fokker-Planck equation