# Diffusion-DFL: Decision-focused Diffusion Models for Stochastic Optimization

arXiv: https://arxiv.org/abs/2510.11590 · HTML: https://mlsanity.com/paper/2510.11590/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 24 of its 34 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 24 of 24)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Diffusion Models for Black-Box Optimization](https://mlsanity.com/paper/2306.07180/) (2023)
- [Decision-Focused Learning: Through the Lens of Learning to Rank](https://mlsanity.com/paper/2112.03609/) (2021)
- [A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization](https://mlsanity.com/paper/2406.01661/) (2024)
- [Second-Order Information in Non-Convex Stochastic Optimization: Power and Limitations](https://mlsanity.com/paper/2006.13476/) (2020)
- [Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints](https://mlsanity.com/paper/2402.18012/) (2024)
- [Gen-DFL: Decision-Focused Generative Learning for Robust Decision Making](https://mlsanity.com/paper/2502.05468/) (2025)
- [Score Function Gradient Estimation to Widen the Applicability of Decision-Focused Learning](https://mlsanity.com/paper/2307.05213/) (2023)
- [Locally Convex Global Loss Network for Decision-Focused Learning](https://mlsanity.com/paper/2403.01875/) (2024)
- [Generalized Decision Focused Learning under Imprecise Uncertainty--Theoretical Study](https://mlsanity.com/paper/2502.17984/) (2025)

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

- [Decision-Focused On-Policy Learning for Contextual Linear Optimization with Partial Feedback](https://mlsanity.com/paper/2606.01081/) (2026)
- [Decision-Weighted Flow Matching for Contextual Stochastic Optimization](https://mlsanity.com/paper/2606.16790/) (2026)
- [Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian](https://mlsanity.com/paper/2605.19391/) (2026)
- [Verify Claims, Not Scores: Evidence-Based Verification of Modular Agents](https://mlsanity.com/paper/2610.01348/) (2026)
- [The Curvature of Regret in Contextual Linear Optimization](https://mlsanity.com/paper/2610.01980/) (2026)

## Abstract (arXiv)

Decision-focused learning (DFL) integrates predictive modeling and optimization by training predictors to optimize the downstream decision target rather than merely minimizing prediction error. To date, existing DFL methods typically rely on deterministic point predictions, which are often insufficient to capture the intrinsic stochasticity of real-world environments. To address this challenge, we propose the first diffusion-based DFL approach, which trains a diffusion model to represent the distribution of uncertain parameters and optimizes the decision by solving a stochastic optimization with samples drawn from the diffusion model. Our contributions are twofold. First, we formulate diffusion DFL using the reparameterization trick, enabling end-to-end training through diffusion. While effective, it is memory and compute-intensive due to the need to differentiate through the diffusion sampling process. Second, we propose a lightweight score function estimator that uses only several forward diffusion passes and avoids backpropagation through the sampling. This follows from our results that backpropagating through stochastic optimization can be approximated by a weighted score function formulation. We empirically show that our diffusion DFL approach consistently outperforms strong baselines in decision quality. The source code for all experiments is available at the project repository: https://github.com/GT-KOALA/Diffusion_DFL.