Accurate and efficient simulation-based inference for massive black-hole binaries with LISA

We develop an accurate simulation-based inference framework for high-mass (greater than or similar to 107M circle dot) black-hole binaries observable by LISA. The method is implemented within the DINGO gravitational-wave parameter-estimation code, extending its application from ground-based detectors to the LISA band. We train a normalizing-flow model using aligned-spin higher-mode waveform models and a low-frequency approximation of the detector response at fixed reference time. After sampling, we importance sample to the true posterior based on the underlying likelihood and prior. We validate performance on simulated signals spanning the signal-to-noise regimes relevant for LISA observations and benchmark our new DINGO implementation against standard methods. We report robust agreement in the inferred posterior distributions up to signal-to-noise ratios of 500. At higher signal-to-noise ratios of 1000, we observe a reduction in sampling efficiency, while still yielding unbiased and tightly localized posteriors that can be used as a starting point for follow-up with traditional methods. The trained flow can generate 20 thousand posterior samples in less than a minute, establishing DINGO as a promising neural inference framework for rapid full-parameter estimation of massive black-hole binaries in the LISA band. The proposed approach allows for straightforward generalizations, including a time-dependent detector response, nonstationary noise artifacts such as gaps and glitches, and low-latency parameter estimations.