# Diffusion Models in Simulation-Based Inference: A Tutorial Review

arXiv: https://arxiv.org/abs/2512.20685 · HTML: https://mlsanity.com/paper/2512.20685/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 34 of its 228 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 34)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Conditional Image Generation with Score-Based Diffusion Models](https://mlsanity.com/paper/2111.13606/) (2021)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Mish: A Self Regularized Non-Monotonic Activation Function](https://mlsanity.com/paper/1908.08681/) (2019)
- [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://mlsanity.com/paper/1804.06788/) (2018)
- [Generator Matching: Generative modeling with arbitrary Markov processes](https://mlsanity.com/paper/2410.20587/) (2024)
- [Target Score Matching](https://mlsanity.com/paper/2402.08667/) (2024)
- [Bayesian Workflow](https://mlsanity.com/paper/2011.01808/) (2020)
- [An Introduction to Flow Matching and Diffusion Models](https://mlsanity.com/paper/2506.02070/) (2025)
- [Contractive Diffusion Probabilistic Models](https://mlsanity.com/paper/2401.13115/) (2024)
- [Benchmarking Invertible Architectures on Inverse Problems](https://mlsanity.com/paper/2101.10763/) (2021)
- [Diffusion Model for Data-Driven Black-Box Optimization](https://mlsanity.com/paper/2403.13219/) (2024)
- [Equilibrium Matching: Generative Modeling with Implicit Energy-Based Models](https://mlsanity.com/paper/2510.02300/) (2025)
- [The Statistical Accuracy of Neural Posterior and Likelihood Estimation](https://mlsanity.com/paper/2411.12068/) (2024)
- [The Curse of Conditions: Analyzing and Improving Optimal Transport for Conditional Flow-Based Generation](https://mlsanity.com/paper/2503.10636/) (2025)
- [Flow Matching with Semidiscrete Couplings](https://mlsanity.com/paper/2509.25519/) (2025)
- [On Fitting Flow Models with Large Sinkhorn Couplings](https://mlsanity.com/paper/2506.05526/) (2025)
- [Simulation-based Bayesian inference under model misspecification](https://mlsanity.com/paper/2503.12315/) (2025)
- [Domain-Adaptive Neural Posterior Estimation for Strong Gravitational Lens Analysis](https://mlsanity.com/paper/2410.16347/) (2024)
- [Bifidelity Parameter Estimation Using Conditional Diffusion Models](https://mlsanity.com/paper/2504.01894/) (2025)
- [Low-Budget Simulation-Based Inference with Bayesian Neural Networks](https://mlsanity.com/paper/2408.15136/) (2024)
- [Machine learning-enabled velocity model building with uncertainty quantification](https://mlsanity.com/paper/2411.06651/) (2024)
- [Conditional Flow Matching for Bayesian Posterior Inference](https://mlsanity.com/paper/2510.09534/) (2025)
- [Predictive variational inference: Learn the predictively optimal posterior distribution](https://mlsanity.com/paper/2410.14843/) (2024)
- [Amortized Bayesian Mixture Models](https://mlsanity.com/paper/2501.10229/) (2025)
- [A COMPASS to Model Comparison and Simulation-Based Inference in Galactic Chemical Evolution](https://mlsanity.com/paper/2507.05060/) (2025)
- [Flow Matching Calibration for Simulation-Based Inference under Model Misspecification](https://mlsanity.com/paper/2509.23385/) (2025)

## Built on by (most cited first, 11 of 11)

- [BayesFlow 2: Multi-Backend Amortized Bayesian Inference in Python](https://mlsanity.com/paper/2602.07098/) (2026)
- [JADAI: Jointly Amortizing Adaptive Design and Bayesian Inference](https://mlsanity.com/paper/2512.22999/) (2025)
- [SAGE: Subsurface AI-driven Geostatistical Extraction with proxy posterior](https://mlsanity.com/paper/2604.00307/) (2026)
- [Overcoming Selection Bias in Statistical Studies With Amortized Bayesian Inference](https://mlsanity.com/paper/2604.18319/) (2026)
- [Inverting Foundation Models of Brain Function with Simulation-Based Inference](https://mlsanity.com/paper/2604.23865/) (2026)
- [StAD: Stein Amortized Divergence for Fast Likelihoods with Diffusion and Flow](https://mlsanity.com/paper/2605.16486/) (2026)
- [GenSBI: Generative Methods for Simulation-Based Inference in JAX](https://mlsanity.com/paper/2605.27499/) (2026)
- [Scalable Diffusion SBI for Compositional Inference under Simulator Misspecification](https://mlsanity.com/paper/2609.36950/) (2026)
- [High-Dimensional Simulation-Based Inference in Latent Spaces](https://mlsanity.com/paper/2609.37381/) (2026)
- [Mitigating Representation Gaps in Amortized Bayesian Inference with Auxiliary Supervision](https://mlsanity.com/paper/2609.39525/) (2026)
- [Semi-Amortized Bayesian Inference with Reusable Local Posteriors](https://mlsanity.com/paper/2610.18945/) (2026)

## Abstract (arXiv)

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.