Flow Matching for Scalable Simulation-Based Inference

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Neural posterior estimation methods based on discrete normalizing flows have become established tools for simulation-based inference (SBI), but scaling them to high-dimensional problems can be challenging. Building on recent advances in generative modeling, we here present flow matching posterior estimation (FMPE), a technique for SBI using continuous normalizing flows. Like diffusion models, and in contrast to discrete flows, flow matching allows for unconstrained architectures, providing enhanced flexibility for complex data modalities. Flow matching, therefore, enables exact density evaluation, fast training, and seamless scalability to large architectures--making it ideal for SBI. We show that FMPE achieves competitive performance on an established SBI benchmark, and then demonstrate its improved scalability on a challenging scientific problem: for gravitational-wave inference, FMPE outperforms methods based on comparable discrete flows, reducing training time by 30% with substantially improved accuracy. Our work underscores the potential of FMPE to enhance performance in challenging inference scenarios, thereby paving the way for more advanced applications to scientific problems.

Maximilian Dax, Jonas Wildberger, Simon Buchholz, Stephen R. Green, Jakob H. Macke, Bernhard Schölkopf · 2023

Related benchmarks

Task	Dataset	Result
Simulation-Based Inference	Hierarchical Gaussian Linear	l-C2ST0.00049	55
Simulation-Based Inference	Hierarchical Two Moons	l-C2ST0.232	55
Simulation-Based Inference	Hierarchical Gaussian Mixture	l-C2ST0.00188	55
Simulation-Based Inference	Hierarchical Gaussian Linear Uniform	l-C2ST0.00158	55
Simulation-Based Inference	Hierarchical SLCP	l-C2ST19	54
Simulation-Based Inference	Hierarchical SIR	l-C2ST0.000241	53
Simulation-Based Inference	SBIBM Gaussian Linear	C2ST0.97	19
Posterior Estimation	SBIBM SLCP	Joint C2ST83	10
Posterior Sampling	SLCP SBI benchmark	C2ST96	7
Posterior Sampling	Gaussian Mixture SBI benchmark	C2ST57	7