# Constraint-Guided Prediction Refinement via Deterministic Diffusion Trajectories

arXiv: https://arxiv.org/abs/2506.12911 · HTML: https://mlsanity.com/paper/2506.12911/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 35 references that are in the map.
- First posted on arXiv 15 Jun 2025.

## Builds on (most cited first, 23 of 23)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [Score-Based Generative Models Detect Manifolds](https://mlsanity.com/paper/2206.01018/) (2022)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Data](https://mlsanity.com/paper/2402.04823/) (2024)
- [Metropolis Sampling for Constrained Diffusion Models](https://mlsanity.com/paper/2307.05439/) (2023)
- [A Unified Framework for Adversarial Attack and Defense in Constrained Feature Space](https://mlsanity.com/paper/2112.01156/) (2021)
- [Training-Free Constrained Generation With Stable Diffusion Models](https://mlsanity.com/paper/2502.05625/) (2025)
- [PowerNet: Multi-agent Deep Reinforcement Learning for Scalable Powergrid Control](https://mlsanity.com/paper/2011.12354/) (2020)
- [Constrained Adaptive Attack: Effective Adversarial Attack Against Deep Neural Networks for Tabular Data](https://mlsanity.com/paper/2406.00775/) (2024)
- [TabularBench: Benchmarking Adversarial Robustness for Tabular Deep Learning in Real-world Use-cases](https://mlsanity.com/paper/2408.07579/) (2024)
- [Constrained Diffusion with Trust Sampling](https://mlsanity.com/paper/2411.10932/) (2024)

## Abstract (arXiv)

Many real-world machine learning tasks require outputs that satisfy hard constraints, such as physical conservation laws, structured dependencies in graphs, or column-level relationships in tabular data. Existing approaches rely either on domain-specific architectures and losses or on strong assumptions on the constraint space, restricting their applicability to linear or convex constraints. We propose a general-purpose framework for constraint-aware refinement that leverages denoising diffusion implicit models (DDIMs). Starting from a coarse prediction, our method iteratively refines it through a deterministic diffusion trajectory guided by a learned prior and augmented by constraint gradient corrections. The approach accommodates a wide class of non-convex and nonlinear equality constraints and can be applied post hoc to any base model. We demonstrate the method in two representative domains: constrained adversarial attack generation on tabular data with column-level dependencies and in AC power flow prediction under Kirchhoff's laws. Across both settings, our diffusion-guided refinement improves both constraint satisfaction and performance while remaining lightweight and model-agnostic.