# Robust Optimization with Diffusion Models for Green Security

arXiv: https://arxiv.org/abs/2503.05730 · HTML: https://mlsanity.com/paper/2503.05730/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 30 of its 60 references that are in the map.
- First posted on arXiv 19 Feb 2025.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [A Unified Game-Theoretic Approach to Multiagent Reinforcement Learning](https://mlsanity.com/paper/1711.00832/) (2017)
- [Practical and Asymptotically Exact Conditional Sampling in Diffusion Models](https://mlsanity.com/paper/2306.17775/) (2023)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Autoregressive Diffusion Model for Graph Generation](https://mlsanity.com/paper/2307.08849/) (2023)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints](https://mlsanity.com/paper/2402.18012/) (2024)
- [Dual-Mandate Patrols: Multi-Armed Bandits for Green Security](https://mlsanity.com/paper/2009.06560/) (2020)
- [Robust Reinforcement Learning Under Minimax Regret for Green Security](https://mlsanity.com/paper/2106.08413/) (2021)
- [Stay Ahead of Poachers: Illegal Wildlife Poaching Prediction and Patrol Planning Under Uncertainty with Field Test Evaluations](https://mlsanity.com/paper/1903.06669/) (2019)
- [MUBen: Benchmarking the Uncertainty of Molecular Representation Models](https://mlsanity.com/paper/2306.10060/) (2023)
- [DyGen: Learning from Noisy Labels via Dynamics-Enhanced Generative Modeling](https://mlsanity.com/paper/2305.19395/) (2023)
- [Double Oracle Algorithm for Computing Equilibria in Continuous Games](https://mlsanity.com/paper/2009.12185/) (2020)
- [Restless and Uncertain: Robust Policies for Restless Bandits via Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2107.01689/) (2021)
- [Cardinality-constrained Distributionally Robust Portfolio Optimization](https://mlsanity.com/paper/2112.12454/) (2021)
- [Exploiting Data and Human Knowledge for Predicting Wildlife Poaching](https://mlsanity.com/paper/1805.05356/) (2018)
- [Randomized Minmax Regret for Combinatorial Optimization Under Uncertainty](https://mlsanity.com/paper/1401.7043/) (2014)

## Built on by (most cited first, 5 of 5)

- [Composite Flow Matching for Reinforcement Learning with Shifted-Dynamics Data](https://mlsanity.com/paper/2505.23062/) (2025)
- [Constrained Diffusion Models with Primal-Dual Inference](https://mlsanity.com/paper/2606.17192/) (2026)
- [Generative AI Against Poaching: Latent Composite Flow Matching for Wildlife Conservation](https://mlsanity.com/paper/2508.14342/) (2025)
- [Generating DDPM-based Samples from Tilted Distributions](https://mlsanity.com/paper/2604.03015/) (2026)
- [DiffNash: Finding Nash Equilibrium in High-Dimensional Continuous Action Spaces with Diffusion Policies](https://mlsanity.com/paper/2610.15932/) (2026)

## Abstract (arXiv)

In green security, defenders must forecast adversarial behavior, such as poaching, illegal logging, and illegal fishing, to plan effective patrols. These behavior are often highly uncertain and complex. Prior work has leveraged game theory to design robust patrol strategies to handle uncertainty, but existing adversarial behavior models primarily rely on Gaussian processes or linear models, which lack the expressiveness needed to capture intricate behavioral patterns. To address this limitation, we propose a conditional diffusion model for adversary behavior modeling, leveraging its strong distribution-fitting capabilities. To the best of our knowledge, this is the first application of diffusion models in the green security domain. Integrating diffusion models into game-theoretic optimization, however, presents new challenges, including a constrained mixed strategy space and the need to sample from an unnormalized distribution to estimate utilities. To tackle these challenges, we introduce a mixed strategy of mixed strategies and employ a twisted Sequential Monte Carlo (SMC) sampler for accurate sampling. Theoretically, our algorithm is guaranteed to converge to an epsilon equilibrium with high probability using a finite number of iterations and samples. Empirically, we evaluate our approach on both synthetic and real-world poaching datasets, demonstrating its effectiveness.