# DiffOPF: Diffusion Solver for Optimal Power Flow

arXiv: https://arxiv.org/abs/2510.14075 · HTML: https://mlsanity.com/paper/2510.14075/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 15 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [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 Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [A Survey on Generative Adversarial Networks: Variants, Applications, and Training](https://mlsanity.com/paper/2006.05132/) (2020)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions](https://mlsanity.com/paper/2205.10129/) (2022)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (2023)
- [DNN-based Policies for Stochastic AC OPF](https://mlsanity.com/paper/2112.02441/) (2021)
- [Lecture Notes on Optimal Power Flow (OPF)](https://mlsanity.com/paper/1811.00943/) (2018)
- [On diffusion posterior sampling via sequential Monte Carlo for zero-shot scaffolding of protein motifs](https://mlsanity.com/paper/2412.05788/) (2024)
- [Universal Graph Learning for Power System Reconfigurations: Transfer Across Topology Variations](https://mlsanity.com/paper/2509.08672/) (2025)
- [GPU-Resident Sparse Direct Linear Solvers for Alternating Current Optimal Power Flow Analysis](https://mlsanity.com/paper/2306.14337/) (2023)
- [Constrained Diffusion Models for Synthesizing Representative Power Flow Datasets](https://mlsanity.com/paper/2506.11281/) (2025)

## Built on by (most cited first, 2 of 2)

- [FMOPF: Latent Flow Matching with Constraint-Aware Interaction Priors for AC Optimal Power Flow](https://mlsanity.com/paper/2607.22788/) (2026)
- [D-IMPL: A Diffusion-based Solver for Parameterized BBOs](https://mlsanity.com/paper/2609.22752/) (2026)

## Abstract (arXiv)

The optimal power flow (OPF) is a multi-valued, non-convex mapping from loads to dispatch setpoints. The variability of system parameters (e.g., admittances, topology) further contributes to the multiplicity of dispatch setpoints for a given load. Existing deep learning OPF solvers are single-valued and thus fail to capture the variability of system parameters unless fully represented in the feature space, which is prohibitive. To solve this problem, we introduce a diffusion-based OPF solver, termed textitDiffOPF, that treats OPF as a conditional sampling problem. The solver learns the joint distribution of loads and dispatch setpoints from operational history, and returns the marginal dispatch distributions conditioned on loads. Unlike single-valued solvers, DiffOPF enables sampling statistically credible warm starts with favorable cost and constraint satisfaction trade-offs. We explore the sample complexity of DiffOPF to ensure the OPF solution within a prescribed distance from the optimization-based solution, and verify this experimentally on power system benchmarks.