  Detecting the coalescences of massive black hole binaries (MBHBs) is one of
the primary targets for space-based gravitational wave observatories such as
LISA, Taiji, and Tianqin. The fast and accurate parameter estimation of merging
MBHBs is of great significance for both astrophysics and the global fitting of
all resolvable sources. However, such analyses entail significant computational
costs. To address these challenges, inspired by the latest progress in
generative models, we proposed a novel artificial intelligence (AI) based
parameter estimation method called Variance Preserving Flow Matching Posterior
Estimation (VPFMPE). Specifically, we utilize triangular interpolation to
maintain variance over time, thereby constructing a transport path for training
continuous normalization flows. Compared to the simple linear interpolation
method used in flow matching to construct the optimal transport path, our
approach better captures continuous temporal variations, making it more
suitable for the parameter estimation of MBHBs. Additionally, we creatively
introduce a parameter transformation method based on the symmetry in the
detector's response function. This transformation is integrated within VPFMPE,
allowing us to train the model using a simplified dataset, and then perform
parameter estimation on more general data, hence also acting as a crucial
factor in improving the training speed. In conclusion, for the first time,
within a comprehensive and reasonable parameter range, we have achieved a
complete and unbiased 11-dimensional rapid inference for MBHBs in the presence
of astrophysical confusion noise using ODE-based generative models. In the
experiments based on simulated data, our model produces posterior distributions
comparable to those obtained by nested sampling.
