# Decision-Aware Training for Sample-Based Generative Models

arXiv: https://arxiv.org/abs/2607.01171 · HTML: https://mlsanity.com/paper/2607.01171/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 1 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [Learning in Implicit Generative Models](https://mlsanity.com/paper/1610.03483/) (2016)
- [Distribution Calibration for Regression](https://mlsanity.com/paper/1905.06023/) (2019)
- [Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration](https://mlsanity.com/paper/2107.05719/) (2021)
- [FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scale](https://mlsanity.com/paper/2507.12144/) (2025)
- [U-Calibration: Forecasting for an Unknown Agent](https://mlsanity.com/paper/2307.00168/) (2023)
- [When Does Optimizing a Proper Loss Yield Calibration?](https://mlsanity.com/paper/2305.18764/) (2023)
- [ArchesWeather & ArchesWeatherGen: a deterministic and generative model for efficient ML weather forecasting](https://mlsanity.com/paper/2412.12971/) (2024)
- [Distributional Diffusion Models with Scoring Rules](https://mlsanity.com/paper/2502.02483/) (2025)
- [Forecaster's Dilemma: Extreme Events and Forecast Evaluation](https://mlsanity.com/paper/1512.09244/) (2015)
- [Smooth Calibration and Decision Making](https://mlsanity.com/paper/2504.15582/) (2025)
- [Three Types of Calibration with Properties and their Semantic and Formal Relationships](https://mlsanity.com/paper/2504.18395/) (2025)
- [Day-Ahead Bidding Strategies for Wind Farm Operators under a One-Price Balancing Scheme](https://mlsanity.com/paper/2505.05153/) (2025)
- [Improved probabilistic regression using diffusion models](https://mlsanity.com/paper/2510.04583/) (2025)

## Abstract (arXiv)

Sample-based generative models are increasingly used for probabilistic forecasting in high-stakes decision settings, yet their training objectives are blind to the decision maker's cost structure. These models are commonly trained with strictly proper scoring rules, such as the energy score, which allocate their training signal in proportion to data density, with no awareness of where forecast errors are most costly for downstream decisions. We therefore propose decision-aware training for sample-based generative models, augmenting the energy score objective with a differentiable decision loss that directly penalises the cost incurred by acting on the model's forecast. This combined loss is theoretically grounded, as the decision loss is itself a proper scoring rule. We compute the decision loss via a differentiable optimisation layer. Its gradient concentrates in cost-sensitive regions of the output space, making the method's effects interpretable and predictable from the cost structure. We validate the method on one synthetic and two real-world tasks. In the synthetic task, the method corrects the mode weights of a learned bimodal distribution; in a wind power dispatch task, it concentrates improvements in the rare but costly tail region, and in a frost protection task, it improves how well the decision costs are anticipated. Our method yields generative models that retain full probabilistic forecasts while being better aligned with the decision maker's specific cost structure.