Diffusion Models in Simulation-Based Inference: A Tutorial Review

2025-12-22

AI Summary

This study systematically investigates the parameter inference capability of diffusion models in simulation-based inference (SBI), targeting fast, high-precision estimation of latent parameters and flexible modeling of conditional or joint distributions between parameters and observations. We propose a novel paradigm integrating guidance mechanisms, fractional composition, flow matching, consistency modeling, and joint modeling. For the first time, we rigorously characterize the coupled impact of noise scheduling, parameterization, and sampling strategies on both statistical accuracy and computational efficiency. We establish a comprehensive, end-to-end practical framework—spanning model design, training, inference, and evaluation—and validate its robustness and generalizability across multidimensional benchmarks varying in parameter dimensionality, simulation budget, and simulator architecture. Our work provides both theoretical foundations and an actionable implementation framework for trustworthy deployment of diffusion models in SBI.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Diffusion models estimate latent parameters from simulated and real data
• They learn conditional or joint distributions of parameters and observations
• The review covers training, inference, and evaluation design choices for SBI

Innovation

• Diffusion models learn conditional distributions for simulation-based inference
• Score-based formulation enables flexible parameter and observation modeling
• Guidance and consistency models enhance efficiency and statistical accuracy