Amortized Bayesian inference (ABI) has emerged as a powerful simulation-based approach for estimating complex mechanistic models, offering fast posterior sampling via generative neural networks. However, extending ABI to hierarchical models, a cornerstone of modern Bayesian analysis, remains a major challenge due to the need to simulate massive data sets and estimate thousands of parameters. In this work, we build on compositional score matching (CSM), a divide-and-conquer strategy for Bayesian updating using diffusion models. To address existing stability issues of CSM in dealing with large data sets, we couple adaptive solvers with a novel, error-damping compositional estimator. Our estimator remains stable even with hundreds of thousands of data points and parameters. We validate our approach on a controlled toy example, a high-dimensional autoregressive model, and a real-world advanced microscopy application involving over 750,000 parameters.
Arruda et al. (Tue,) studied this question.