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Diffusion-Based Scenario Tree Generation for Multivariate Time Series Prediction and Multistage Stochastic Optimization

Stelios Zarifis, Ioannis Kordonis, Petros Maragos

TL;DR

The paper addresses decision-making under uncertainty in multistage settings by introducing Diffusion Scenario Tree (DST), which builds non-anticipative, hierarchical scenario trees from diffusion-based probabilistic forecasts (e.g., TimeGrad) to guide multistage MPC. DST samples multiple future trajectories, clusters them into a tractable set of representative branches, and propagates them through a horizon while enforcing non-anticipativity, enabling robust optimization in partially observable domains. Empirically, DST-based MPC outperforms standard MPC, VAR/LSTM-based scenario trees, and model-free RL in energy arbitrage with a Battery Energy Storage System in NYISO, achieving high rewards and stable performance due to better handling of multimodal uncertainty. The work advances the integration of modern probabilistic forecasting with operations research, offering a scalable, structured approach to uncertainty modeling with clear practical impact for energy systems and other stochastic control problems.

Abstract

Stochastic forecasting is critical for efficient decision-making in uncertain systems, such as energy markets and finance, where estimating the full distribution of future scenarios is essential. We propose Diffusion Scenario Tree (DST), a general framework for constructing scenario trees using diffusion-based probabilistic forecasting models to provide a structured model of system evolution for control tasks. DST recursively samples future trajectories and organizes them into a tree via clustering, ensuring non-anticipativity (decisions depending only on observed history) at each stage, offering a superior representation of uncertainty compared to using predictive models solely for forecasting system evolution. We integrate DST into Model Predictive Control (MPC) and evaluate it on energy arbitrage in New York State's day-ahead electricity market. Experimental results show that our approach significantly outperforms the same optimization algorithms that use scenario trees generated by more conventional models. Furthermore, using DST for stochastic optimization yields more efficient decision policies by better handling uncertainty than deterministic and stochastic MPC variants using the same diffusion-based forecaster, and simple Model-Free Reinforcement Learning (RL) baselines.

Diffusion-Based Scenario Tree Generation for Multivariate Time Series Prediction and Multistage Stochastic Optimization

TL;DR

The paper addresses decision-making under uncertainty in multistage settings by introducing Diffusion Scenario Tree (DST), which builds non-anticipative, hierarchical scenario trees from diffusion-based probabilistic forecasts (e.g., TimeGrad) to guide multistage MPC. DST samples multiple future trajectories, clusters them into a tractable set of representative branches, and propagates them through a horizon while enforcing non-anticipativity, enabling robust optimization in partially observable domains. Empirically, DST-based MPC outperforms standard MPC, VAR/LSTM-based scenario trees, and model-free RL in energy arbitrage with a Battery Energy Storage System in NYISO, achieving high rewards and stable performance due to better handling of multimodal uncertainty. The work advances the integration of modern probabilistic forecasting with operations research, offering a scalable, structured approach to uncertainty modeling with clear practical impact for energy systems and other stochastic control problems.

Abstract

Stochastic forecasting is critical for efficient decision-making in uncertain systems, such as energy markets and finance, where estimating the full distribution of future scenarios is essential. We propose Diffusion Scenario Tree (DST), a general framework for constructing scenario trees using diffusion-based probabilistic forecasting models to provide a structured model of system evolution for control tasks. DST recursively samples future trajectories and organizes them into a tree via clustering, ensuring non-anticipativity (decisions depending only on observed history) at each stage, offering a superior representation of uncertainty compared to using predictive models solely for forecasting system evolution. We integrate DST into Model Predictive Control (MPC) and evaluate it on energy arbitrage in New York State's day-ahead electricity market. Experimental results show that our approach significantly outperforms the same optimization algorithms that use scenario trees generated by more conventional models. Furthermore, using DST for stochastic optimization yields more efficient decision policies by better handling uncertainty than deterministic and stochastic MPC variants using the same diffusion-based forecaster, and simple Model-Free Reinforcement Learning (RL) baselines.

Paper Structure

This paper contains 13 sections, 4 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Methodology
  4. Problem Definition
  5. Diffusion-Based Forecasting
  6. Scenario Tree-Based Stochastic Optimization
  7. Diffusion Scenario Tree
  8. Solving the Multistage Stochastic MPC
  9. Results
  10. DST-based MPC vs. Standard MPC
  11. DST-based MPC vs. LSTM- and VAR-based MPC
  12. DST-based MPC vs. Model-Free RL
  13. Conclusion

Figures (2)

  • Figure 1: Visualization of a Scenario Tree that discretizes the probability distribution of the future steps.
  • Figure 2: Strategy planned by Scenario tree-based MPC. Dotted lines depict the forecasted stochastic component, organized in a tree. Gray line shows the actual stochastic part evolution, blue line represents the optimized actions for the first stage, and dashed lines the optimized actions across branches.