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A Review of Diffusion-based Simulation-Based Inference Foundations and Applications in Non-Ideal Data Scenarios

H Rosso, T Mayo - arXiv preprint arXiv:2512.23748, 2025 - arxiv.org
Physics paper cs.LG Suggest

… The challenge of performing inference without tractable likelihoods motivates simulation-based inference (SBI), which directly estimates posterior distributions over …

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@article{2512.23748v1,
Author        = {Haley Rosso and Talea Mayo},
Title         = {A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios},
Eprint        = {2512.23748v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {cs.LG},
Abstract      = {For complex simulation problems, inferring parameters of scientific interest often precludes the use of classical likelihood-based techniques due to intractable likelihood functions. Simulation-based inference (SBI) methods forego the need for explicit likelihoods by directly utilizing samples from the simulator to learn posterior distributions over parameters $\mathbfθ$ given observed data $\mathbf{x}_{\text{o}}$. Recent work has brought attention to diffusion models -- a type of generative model rooted in score matching and reverse-time stochastic dynamics -- as a flexible framework SBI tasks. This article reviews diffusion-based SBI from first principles to applications in practice. We first recall the mathematical foundations of diffusion modeling (forward noising, reverse-time SDE/ODE, probability flow, and denoising score matching) and explain how conditional scores enable likelihood-free posterior sampling. We then examine where diffusion models address pain points of normalizing flows in neural posterior/likelihood estimation and where they introduce new trade-offs (e.g., iterative sampling costs). The key theme of this review is robustness of diffusion-based SBI in non-ideal conditions common to scientific data: misspecification (mismatch between simulated training data and reality), unstructured or infinite-dimensional observations, and missingness. We synthesize methods spanning foundations drawing from Schrodinger-bridge formulations, conditional and sequential posterior samplers, amortized architectures for unstructured data, and inference-time prior adaptation. Throughout, we adopt consistent notation and emphasize conditions and caveats required for accurate posteriors. The review closes with a discussion of open problems with an eye toward applications of uncertainty quantification for probabilistic geophysical models that may benefit from diffusion-based SBI.},
Year          = {2025},
Month         = {Dec},
Url           = {http://arxiv.org/abs/2512.23748v1},
File          = {2512.23748v1.pdf}
}

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