When strongly lensed gravitational waves pass through the stellar field of a lensing galaxy, they acquire additional phase and amplitude modulations from gravitational microlensing by stars and stellar remnants along the line of sight. These microlensed waveforms depend on the masses and positions of thousands or more of the most relevant stars required for numerical convergence of the wave-optics diffraction integral, so that their deterministic reconstruction from the data is computationally prohibitive. We formulate the detection and parameter estimation of such events as a stochastic inference problem and propose a solution with the implementation of normalizing flows. As a proof of principle, we use the inferred surrogate microlensing parameters to identify microlensing signatures and show that 10.2% of microlensed events can be detected at $\ge 3\sigma$ significance with third-generation gravitational-wave detector networks for source redshifts $z_s\le 2$. The correlation between the surrogate parameters and the density of the underlying stellar field further connects microlensing detection to the properties of the lensing galaxy. This approach opens the door to probing microlensing effects and the properties of the underlying stellar fields. Beyond microlensed gravitational waves, a similar construction may also be applied to other intrinsically stochastic inference problems, such as detecting postmerger gravitational waves from binary neutron star coalescence and signals from core-collapse supernovae.

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• Gravitational waves