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

We develop an accurate simulation-based inference framework for high-mass ($\gtrsim\!10^7 \rm{M_\odot}$) 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 $\sim\!500$. At higher signal-to-noise ratios of $\sim\!1000$, 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, non-stationary noise artifacts such as gaps and glitches, and low-latency parameter estimations.