# Generative Monte Carlo Sampling for Constant-Cost Particle Transport

arXiv: https://arxiv.org/abs/2512.13965 · HTML: https://mlsanity.com/paper/2512.13965/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 16 Dec 2025.

## Builds on (most cited first, 7 of 7)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [High Energy Density Radiative Transfer in the Diffusion Regime with Fourier Neural Operators](https://mlsanity.com/paper/2405.04003/) (2024)

## Built on by (most cited first, 1 of 1)

- [BRICKS: Compositional Neural Markov Kernels for Zero-Shot Radiation-Matter Simulation](https://mlsanity.com/paper/2605.06591/) (2026)

## Abstract (arXiv)

We present Generative Monte Carlo (GMC), a novel paradigm for particle transport simulation that integrates generative artificial intelligence directly into the stochastic solution of the linear Boltzmann equation. By reformulating the cell-transmission problem as a conditional generation task, we train neural networks using conditional flow matching to sample particle exit states, including position, direction, and path length, without simulating scattering histories. The method employs optical coordinate scaling, enabling a single trained model to generalize across any material. We validate GMC on two canonical benchmarks, namely a heterogeneous lattice problem characteristic of nuclear reactor cores and a linearized hohlraum geometry representative of high-energy density radiative transfer. Results demonstrate that GMC preserves the statistical fidelity of standard Monte Carlo, exhibiting the expected 1/√N convergence rate while maintaining accurate scalar flux profiles. While standard Monte Carlo computational cost scales linearly with optical thickness in the diffusive limit, GMC achieves constant O(1) cost per cell transmission, yielding order-of-magnitude speedups in optically thick regimes. This framework strategically aligns particle transport with modern computing architectures optimized for neural network inference, positioning transport codes to leverage ongoing advances in AI hardware and algorithms.