Diffusion Models in Simulation-Based Inference: A Tutorial Review
stat.ML, cs.LG, stat.ME
Submitted: 2025-12-22
Updated: 2026-10-15
Comments: Accepted in TMLR with Survey Certification
Project page: https://ml4physicalsciences.github.io/2024/files/NeurIPS_ML4PS_2024_26.pdf
License: http://creativecommons.org/licenses/by/4.0/
The gist: Diffusion models have recently emerged as powerful learners for simulation-based inference (SBI), enabling fast and accurate estimation of latent parameters from simulated and real data.
Terminology
Abstract
Diffusion models have recently emerged as powerful learners for simulation-based inference (SBI), enabling fast and accurate estimation of latent parameters from simulated and real data. Their score-based formulation offers a flexible way to learn conditional or joint distributions over parameters and observations, thereby providing a versatile solution to various modeling problems. In this tutorial review, we synthesize recent developments on diffusion models for SBI, covering design choices for training, inference, and evaluation. We highlight opportunities created by various concepts such as guidance, score composition, flow matching, consistency models, and joint modeling. Furthermore, we discuss how efficiency and statistical accuracy are affected by noise schedules, parameterizations, and samplers. Finally, we illustrate these concepts with case studies across parameter dimensionalities, simulation budgets, and model types, and outline open questions for future research.
Sources
- Layer Normalization
- Conformal C2ST: Turning weak classifiers into strong two-sample tests
- Amortised and provably-robust simulation-based inference
- Mixed neural posterior estimation for simulators with discrete and continuous parameters
- The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generation
- A Survey on Diffusion Models for Inverse Problems
- Target Score Matching
- Low-Budget Simulation-Based Inference with Bayesian Neural Networks
- Causal Posterior Estimation
- The Statistical Accuracy of Neural Posterior and Likelihood Estimation
- Bayesian Workflow
- Do Diffusion Models Dream of Electric Planes? Discrete and Continuous Simulation-Based Inference for Aircraft Design
- Scalable Simulation-Based Model Inference with Test-Time Complexity Control
- A COMPASS to Model Comparison and Simulation-Based Inference in Galactic Chemical Evolution
- An Introduction to Flow Matching and Diffusion Models
- Generator Matching: Generative modeling with arbitrary Markov processes
- Conditional Flow Matching for Bayesian Posterior Inference
- Simulation-based Inference via Langevin Dynamics with Score Matching
- Gotta Go Fast When Generating Data with Score-Based Models
- Simulation-based Bayesian inference under model misspecification
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