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Julia Linhart

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TMLR Journal 2026 Journal Article

Diffusion posterior sampling for simulation-based inference in tall data settings

Julia Linhart
Gabriel Cardoso
Alexandre Gramfort
Sylvain Le Corff
Pedro L. C. Rodrigues

Identifying the parameters of a non-linear model that best explain observed data is a core task across scientific fields. When such models rely on complex simulators, evaluating the likelihood is typically intractable, making traditional inference methods such as MCMC inapplicable. Simulation-based inference (SBI) addresses this by training deep generative models to approximate the posterior distribution over parameters using simulated data. In this work, we consider the tall data setting, where multiple independent observations provide additional information, allowing sharper posteriors and improved parameter identifiability. Building on the flourishing score-based diffusion literature, F-NPSE (Geffner et al., 2023) estimates the tall data posterior by composing individual scores from a neural network trained only for a single context observation. This enables more flexible and simulation-efficient inference than alternative approaches for tall datasets in SBI. However, it relies on costly Langevin dynamics during sampling. We propose a new algorithm that eliminates the need for Langevin steps by explicitly approximating the diffusion process of the tall data posterior. Our method retains the advantages of compositional score-based inference while being significantly faster and more stable than F-NPSE. We demonstrate its improved performance on toy problems and standard SBI benchmarks, and showcase its scalability by applying it to a complex real-world model from computational neuroscience.

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NeurIPS Conference 2023 Conference Paper

L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inference

Julia Linhart
Alexandre Gramfort
Pedro Rodrigues

Many recent works in simulation-based inference (SBI) rely on deep generative models to approximate complex, high-dimensional posterior distributions. However, evaluating whether or not these approximations can be trusted remains a challenge. Most approaches evaluate the posterior estimator only in expectation over the observation space. This limits their interpretability and is not sufficient to identify for which observations the approximation can be trusted or should be improved. Building upon the well-known classifier two-sample test (C2ST), we introduce $\ell$-C2ST, a new method that allows for a local evaluation of the posterior estimator at any given observation. It offers theoretically grounded and easy to interpret -- e. g. graphical -- diagnostics, and unlike C2ST, does not require access to samples from the true posterior. In the case of normalizing flow-based posterior estimators, $\ell$-C2ST can be specialized to offer better statistical power, while being computationally more efficient. On standard SBI benchmarks, $\ell$-C2ST provides comparable results to C2ST and outperforms alternative local approaches such as coverage tests based on highest predictive density (HPD). We further highlight the importance of local evaluation and the benefit of interpretability of $\ell$-C2ST on a challenging application from computational neuroscience.

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