Reusable Conditional Resampling via Flow Matching for Constraint-Based Causal Discovery

Constraint-based causal discovery requires a large number of conditional independence (CI) tests. In nonlinear and high-dimensional settings, generative CI methods offer strong expressive power, but often suffer from high per test cost and limited reusability across the many query dependent conditional resampling tasks arising in graph search. We propose a generative nonlinear CI testing and graph search framework for PC-style causal discovery. First, we develop the Flow Matching based Conditional Independence Test (FMCIT), which combines joint flow matching modeling with conditional imputation to reformulate generative CI testing from query specific conditional modeling into a conditional resampling process that can be reused across queries. This allows the same generative model to repeatedly generate the randomized copies required by CI testing throughout the entire graph search procedure. We then introduce GPC‑FMCIT, which embeds FMCIT into a guided PC pipeline with screening, guidance, refinement, and orientation. By using low-cost screening to shrink the search space, constructing edge-specific candidate conditioning sets from local graph structure, and invoking FMCIT only in a budget-controlled refinement stage, GPC-FMCIT reduces both the deployment cost of individual nonlinear CI queries and the overall query complexity. Experiments on synthetic datasets and real-data analyses show that the proposed method achieves a strong accuracy--efficiency trade-off under nonlinear and high-dimensional structures. Overall, our results suggest that, through the joint design of reusable conditional resampling and controlled graph search, generative nonlinear CI testing can become a practical system level module for high‑dimensional PC‑style causal discovery.