Tokenised Flow Matching for Hierarchical Simulation Based Inference

arXiv cs.LG / 4/23/2026

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Key Points

The paper targets a major practical bottleneck in Simulation Based Inference (SBI): expensive simulator evaluations, especially in hierarchical models.
It introduces likelihood factorisation (LF) training that learns per-site neural surrogates from single-site simulations and then assembles synthetic multi-site observations for amortised inference of the full hierarchical posterior.
Building on LF, the authors propose Tokenised Flow Matching for Posterior Estimation (TFMPE), which uses tokenised flow matching to handle function-valued observations under likelihood factorisation.
To measure progress systematically, they also release a benchmark for hierarchical SBI and validate TFMPE on both the benchmark and realistic infectious-disease and computational fluid dynamics models.
Results indicate TFMPE produces well-calibrated posteriors while lowering computational cost compared with prior hierarchical SBI approaches.

Abstract

The cost of simulator evaluations is a key practical bottleneck for Simulation Based Inference (SBI). In hierarchical settings with shared global parameters and exchangeable site-level parameters and observations, this structure can be exploited to improve simulation efficiency. Existing hierarchical SBI approaches factorise the posterior yet still simulate across multiple sites per training sample; We instead explore likelihood factorisation (LF) to train from single-site simulations. In LF sampling we learn a per-site neural surrogate of the simulator and then assemble synthetic multi-site observations to amortise inference for the full hierarchical posterior. Building on this, we propose Tokenised Flow Matching for Posterior Estimation (TFMPE), a tokenised flow matching approach that supports function-valued observations through likelihood factorisation. To enable systematic evaluation, we introduce a benchmark for hierarchical SBI. We validate TFMPE on this benchmark and on realistic infectious disease and computational fluid dynamics models, finding well-calibrated posteriors while reducing computational cost.