Noise-Blind Flow Matching for Misspecified Simulation-Based Inference

In this paper we deal with the problem of misspecified simulation-based inference (SBI), which occurs when the forward process is only approximately known. Oftentimes, in the literature a calibration set is used to nudge the posterior towards the noisy measurements. Inspired by time-unconditional flow matching and diffusion methods, we develop noise-blind flow matching (NBFM) for misspecified SBI. NBFM proceeds in two stages: first, we learn the noise-free posterior distribution, and then learn a noise-blind sampler from the noisy to the clean measurements. This allows us to run purely synthetic training without the need for MCMC or a calibration set. Across three learned benchmarks, NBFM yields lower posterior sliced-Wasserstein error than direct FMPE and than FMCPE using up to $5{,}000$ paired calibration samples.