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Neural operators can now learn directly from noisy, low-cost Monte Carlo estimates, achieving $10^4$-$10^5\times$ speedups for particle transport problems without sacrificing accuracy.
This work introduces PosteriorBench, a benchmark for evaluating the distributional accuracy of generative inverse solvers, and reveals substantial distribution-matching gaps across current solvers, while showing that neural operators improve resolution robustness, and guidance weights and generation noise are key to posterior-variance calibration.