Two Phase Rapid Simulation Based Inference with Differentiable Simulators

We introduce Rapid Simulation Based Inference (RSBI), a diffusion-based variational approach to likelihood-free Bayesian inference that achieves high posterior sample efficiency under large and multi-dimensional prior-to-posterior volumes. RSBI builds on recent advances in Schrödinger Bridge (SB) diffusion sampling to handle multi-modal posteriors, with the likelihood supplied either by a neural ratio estimator or kernal surrogate via a differentiable simulator. Furthermore, a key observation is that an appropriate surrogate likelihood gives a proposal distribution covering most of the generally multi-modal posterior mass, replacing the sequential rounds of standard methods with a one-shot proposal step. Subsequent NRE refinement recovers exact inference under the simulator and original model prior. As a variational method, RSBI does not suffer from prior leakage and implicit target drift commonly observed in standard sequential posterior estimation methods. To improve mode coverage we optionally utilize the well-tempered meta-dynamics framework, which also provides a mechanism through which to encourage exploration of the prior volume. We observe strong performance not only on standard SBI benchmarks, but also as prior volume is scaled up to 2500 times the original, achieving a performance degradation of only $\sim$5% on the two moons benchmark under a highly constrained simulation budget. Additionally, we evaluate RSBI's potential for gravitational wave ring-down posterior estimation, highlighting a real-world use-case where our method excels.