Compositional score-based approaches to simulation-based inference (SBI) approximate the posterior over a shared parameter given $n$ independent observations by aggregating individually learned posterior scores: currently, there are two main propositions of such methods (Geffner et al. (2023), Linhart et al. (2026)). As the resulting composite score does not correspond to the score of any distribution along the forward diffusion path of the true multi-observation posterior, sampling from it via a reverse SDE leads to an irreducible bias. Annealed Langevin dynamics provides a principled alternative: it treats the composite score as the genuine score of a sequence of tractable bridging densities and samples from them in succession. When properly tuned, it could lead to a controllable bias. However, its hyperparameters, namely step sizes, the number of steps per level, and the number of annealing levels, have so far been chosen empirically. We derive Wasserstein bounds for annealed Langevin with approximate scores and translate them into explicit decision rules for these hyperparameters that guarantee a prescribed sampling accuracy, while highlighting different theoretical aspects of each composite score formulation. In the Gaussian setting, we obtain closed-form expressions for all relevant quantities and prove that the bridging densities of Linhart et al. (2026) consistently admit larger step sizes and require fewer total Langevin steps than those of Geffner et al. (2023). Furthermore, we show empirically that the tuning obtained in the Gaussian setting generalizes to more complex problems, thus providing a well-understood and theoretically grounded starting point for practitioners using compositional score-based approaches.

NVI learns proposals by optimizing a divergence at each level of nesting.

Sampling from high dimensional, multimodal distributions remains a fundamental challenge across domains such as statistical Bayesian inference and physics based machine learning. In this paper, we propose Annealing Flow, a continuous normalizing flow based approach designed to sample from high dimensional and multimodal distributions. The key idea is to learn a continuous normalizing flow based transport map, guided by annealing, to transition samples from an easy to sample distribution to the target distribution, facilitating effective exploration of modes in high dimensional spaces. Unlike many existing methods, AF training does not rely on samples from the target distribution. AF ensures effective and balanced mode exploration, achieves linear complexity in sample size and dimensions, and circumvents inefficient mixing times. We demonstrate the superior performance of AF compared to state of the art methods through extensive experiments on various challenging distributions and real world datasets, particularly in high-dimensional and multimodal settings. We also highlight the potential of AF for sampling the least favorable distributions.

Reliability updating refers to a problem that integrates Bayesian updating technique with structural reliability analysis and cannot be directly solved by structural reliability methods (SRMs) when it involves equality information. The state-of-the-art approaches transform equality information into inequality information by introducing an auxiliary standard normal parameter. These methods, however, encounter the loss of computational efficiency due to the difficulty in finding the maximum of the likelihood function, the large coefficient of variation (COV) associated with the posterior failure probability and the inapplicability to dynamic updating problems where new information is constantly available. To overcome these limitations, this paper proposes an innovative method called RU-SAIS (reliability updating using sequential adaptive importance sampling), which combines elements of sequential importance sampling and K-means clustering to construct a series of important sampling densities (ISDs) using Gaussian mixture. The last ISD of the sequence is further adaptively modified through application of the cross entropy method. The performance of RU-SAIS is demonstrated by three examples. Results show that RU-SAIS achieves a more accurate and robust estimator of the posterior failure probability than the existing methods such as subset simulation.

We develop nested variational inference (NVI), a family of methods that learn proposals for nested importance samplers by minimizing an forward or reverse KL divergence at each level of nesting. NVI is applicable to many commonly-used importance sampling strategies and provides a mechanism for learning intermediate densities, which can serve as heuristics to guide the sampler. Our experiments apply NVI to (a) sample from a multimodal distribution using a learned annealing path (b) learn heuristics that approximate the likelihood of future observations in a hidden Markov model and (c) to perform amortized inference in hierarchical deep generative models. We observe that optimizing nested objectives leads to improved sample quality in terms of log average weight and effective sample size.