From Thousands of Hours to Seconds: Fast Generative Models for Gravitational-Wave Populations

From Thousands of Hours to Seconds: Fast Generative Models for Gravitational-Wave Populations Gravitational-wave (GW) observations provide a unique probe of the underlying massive-star population, but extracting this information requires modeling how massive stars evolve into merging compact binaries across cosmic time. Forward population-synthesis frameworks that couple binary evolution to cosmic star-formation and metallicity histories are therefore needed to connect observed merger catalogs to the astrophysical parameters governing stellar populations. However, these simulations are prohibitively computationally expensive: exploring even modest grids of formation channels and astrophysical parameters can require the generation of hundreds of millions of simulated mergers and consume tens of thousands of CPU-hours. We present PLANT (Population synthesis with Learned Astrophysical geNerative models for gravitaTional-wave populations), the first conditional generative modeling framework that replaces repeated population-synthesis sampling with fast neural emulators of GW merger populations. We first generate a large training dataset by running population-synthesis simulations across a broad grid of astrophysical hyperparameters, producing merger catalogs that span the Synthetic-Stellar-Pop-Convolve (SSPC) parameter space. SSPC combines binary population-synthesis predictions with models of cosmic star-formation and metallicity evolution to predict the observable distribution of compact-binary mergers across cosmic time. The model learns to generate merger populations conditioned on these parameters, enabling amortized simulation without rerunning expensive forward models. We train on approximately 3.75×10^8 simulated mergers and investigate two complementary generative approaches: (i) conditional flow matching (CFM), which learns deterministic probability-flow trajectories using optimal-transport-inspired paths, and (ii) score-based diffusion models, which learn stochastic denoising dynamics for population generation. Both approaches model the conditional distribution of chirp mass, mass ratio, and redshift given the population-synthesis parameters. We benchmark against a Naive Bayes grid emulator baseline and evaluate distributional fidelity and posterior recovery on LIGO-VIRGO-KAGRA observed gravitational-wave data. The learned emulator accurately reproduces marginal and joint distributions across astrophysical regimes while achieving orders-of-magnitude speedups over direct population synthesis. This work establishes conditional generative modeling via flow matching and diffusion as a scalable surrogate for gravitational-wave population synthesis, enabling rapid generation of physically consistent merger populations for large-scale astrophysical analysis.