High-fidelity simulation of particle–matter interactions provides the essential theoretical reference for diverse physics disciplines, yet generating synthetic datasets at the scale of current and future experiments has become prohibitive. Here, we introduce PHIN-GAN, a novel physics-informed generative adversarial network designed to address this challenge. We derive a set of analytical probability density functions, that effectively describe the "straggling function" identified with Landau. For the first time, this enables their continuous evaluation across the entire phase-space. These analytical forms are leveraged to enforce a parametric distribution-level learning objective. Rooted in first principles, PHIN-GAN offers an interpretable and scalable proof-of-concept approach for a statistically indistinguishable surrogate generative model of the standard-bearer for simulating such interactions, namely GEANT4, at a fraction of the computational cost.