# DDM-Lag : A Diffusion-based Decision-making Model for Autonomous Vehicles with Lagrangian Safety Enhancement

arXiv: https://arxiv.org/abs/2401.03629 · HTML: https://mlsanity.com/paper/2401.03629/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 26 of its 47 references that are in the map.
- First posted on arXiv 8 Jan 2024.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Deep reinforcement learning methods / [RL for autonomous driving and traffic](https://mlsanity.com/deeprl/rl-for-autonomous-driving-and-traffic/)

## Builds on (most cited first, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Decision Transformer: Reinforcement Learning via Sequence Modeling](https://mlsanity.com/paper/2106.01345/) (2021)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [Off-Policy Deep Reinforcement Learning without Exploration](https://mlsanity.com/paper/1812.02900/) (2018)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [A Minimalist Approach to Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06860/) (2021)
- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [MetaDrive: Composing Diverse Driving Scenarios for Generalizable Reinforcement Learning](https://mlsanity.com/paper/2109.12674/) (2021)
- [Imitating Human Behaviour with Diffusion Models](https://mlsanity.com/paper/2301.10677/) (2023)
- [Driving with LLMs: Fusing Object-Level Vector Modality for Explainable Autonomous Driving](https://mlsanity.com/paper/2310.01957/) (2023)
- [DiLu: A Knowledge-Driven Approach to Autonomous Driving with Large Language Models](https://mlsanity.com/paper/2309.16292/) (2023)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [Diffusion Model is an Effective Planner and Data Synthesizer for Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2305.18459/) (2023)
- [Learning to Walk in the Real World with Minimal Human Effort](https://mlsanity.com/paper/2002.08550/) (2020)
- [Synthetic Experience Replay](https://mlsanity.com/paper/2303.06614/) (2023)
- [Challenges and Countermeasures for Adversarial Attacks on Deep Reinforcement Learning](https://mlsanity.com/paper/2001.09684/) (2020)
- [MTD-GPT: A Multi-Task Decision-Making GPT Model for Autonomous Driving at Unsignalized Intersections](https://mlsanity.com/paper/2307.16118/) (2023)
- [Driving in Dense Traffic with Model-Free Reinforcement Learning](https://mlsanity.com/paper/1909.06710/) (2019)
- [Towards Socially Responsive Autonomous Vehicles: A Reinforcement Learning Framework with Driving Priors and Coordination Awareness](https://mlsanity.com/paper/2309.09726/) (2023)

## Built on by (most cited first, 11 of 11)

- [Foundation Models for Spatio-Temporal Data Science: A Tutorial and Survey](https://mlsanity.com/paper/2503.13502/) (2025)
- [Diffusion Policy Attacker: Crafting Adversarial Attacks for Diffusion-based Policies](https://mlsanity.com/paper/2405.19424/) (2024)
- [Imagine-2-Drive: Leveraging High-Fidelity World Models via Multi-Modal Diffusion Policies](https://mlsanity.com/paper/2411.10171/) (2024)
- [Low-Bitwidth Floating Point Quantization for Efficient High-Quality Diffusion Models](https://mlsanity.com/paper/2408.06995/) (2024)
- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [Prompt-Consistency Image Generation (PCIG): A Unified Framework Integrating LLMs, Knowledge Graphs, and Controllable Diffusion Models](https://mlsanity.com/paper/2406.16333/) (2024)
- [Embedding Space Selection for Detecting Memorization and Fingerprinting in Generative Models](https://mlsanity.com/paper/2407.21159/) (2024)
- [DiffMVR: Diffusion-based Automated Multi-Guidance Video Restoration](https://mlsanity.com/paper/2411.18745/) (2024)
- [Enhance the Safety in Reinforcement Learning by ADRC Lagrangian Methods](https://mlsanity.com/paper/2601.18142/) (2026)
- [Evaluation as Evolution: Transforming Adversarial Diffusion into Closed-Loop Curricula for Autonomous Vehicles](https://mlsanity.com/paper/2604.07378/) (2026)
- [Off the Rails: Hijacking the Scoring Head in Generative End-to-End Driving Planners with Safety-Violating Adversarial Perturbations](https://mlsanity.com/paper/2606.30807/) (2026)

## Abstract (arXiv)

Decision-making stands as a pivotal component in the realm of autonomous vehicles (AVs), playing a crucial role in navigating the intricacies of autonomous driving. Amidst the evolving landscape of data-driven methodologies, enhancing decision-making performance in complex scenarios has emerged as a prominent research focus. Despite considerable advancements, current learning-based decision-making approaches exhibit potential for refinement, particularly in aspects of policy articulation and safety assurance. To address these challenges, we introduce DDM-Lag, a Diffusion Decision Model, augmented with Lagrangian-based safety enhancements. This work conceptualizes the sequential decision-making challenge inherent in autonomous driving as a problem of generative modeling, adopting diffusion models as the medium for assimilating patterns of decision-making. We introduce a hybrid policy update strategy for diffusion models, amalgamating the principles of behavior cloning and Q-learning, alongside the formulation of an Actor-Critic architecture for the facilitation of updates. To augment the model's exploration process with a layer of safety, we incorporate additional safety constraints, employing a sophisticated policy optimization technique predicated on Lagrangian relaxation to refine the policy learning endeavor comprehensively. Empirical evaluation of our proposed decision-making methodology was conducted across a spectrum of driving tasks, distinguished by their varying degrees of complexity and environmental contexts. The comparative analysis with established baseline methodologies elucidates our model's superior performance, particularly in dimensions of safety and holistic efficacy.