Cosmic voids contain higher-order cosmological information and are of interest for astroparticle physics. Finding genuine matter underdensities in sparse galaxy surveys is, however, an underconstrained problem. Traditional void finding algorithms produce deterministic void catalogs, neglecting the probabilistic nature of the problem. We present a method to sample from the stochastic mapping from galaxy catalogs to arbitrary void definitions. Our algorithm uses a deep graph neural network to evolve "test particles" according to a flow-matching objective. We demonstrate the method in a simplified example setting but outline steps to generalize it towards practically usable void finders. Trained on a deterministic teacher, the model performs well but has considerable stochasticity which we interpret as regularization. Cosmological information in the predicted void catalogs outperforms the teacher. On the one hand, our method can cheaply emulate existing void finders with apparently useful regularization. More importantly, it also allows us to find the Bayes-optimal mapping between observed galaxies and any void definition. This includes definitions operating at the level of simulated matter density and velocity fields.

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