# Diffusion-ES: Gradient-free Planning with Diffusion for Autonomous Driving and Zero-Shot Instruction Following

arXiv: https://arxiv.org/abs/2402.06559 · HTML: https://mlsanity.com/paper/2402.06559/

## Key facts

- Cited by 42 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 58 of its 73 references that are in the map.
- First posted on arXiv 9 Feb 2024.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- End-to-end autonomous driving / [Imitation-learning end-to-end planners](https://mlsanity.com/driving/imitation-learning-end-to-end-planners/)

## Builds on (most cited first, 30 of 58)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Pre-train, Prompt, and Predict: A Systematic Survey of Prompting Methods in Natural Language Processing](https://mlsanity.com/paper/2107.13586/) (2021)
- [Code as Policies: Language Model Programs for Embodied Control](https://mlsanity.com/paper/2209.07753/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Language Models as Zero-Shot Planners: Extracting Actionable Knowledge for Embodied Agents](https://mlsanity.com/paper/2201.07207/) (2022)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [VoxPoser: Composable 3D Value Maps for Robotic Manipulation with Language Models](https://mlsanity.com/paper/2307.05973/) (2023)
- [GAIA-1: A Generative World Model for Autonomous Driving](https://mlsanity.com/paper/2309.17080/) (2023)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Learning Universal Policies via Text-Guided Video Generation](https://mlsanity.com/paper/2302.00111/) (2023)
- [Visual Programming: Compositional visual reasoning without training](https://mlsanity.com/paper/2211.11559/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [NuPlan: A closed-loop ML-based planning benchmark for autonomous vehicles](https://mlsanity.com/paper/2106.11810/) (2021)
- [End-to-end Driving via Conditional Imitation Learning](https://mlsanity.com/paper/1710.02410/) (2017)
- [DriveGPT4: Interpretable End-to-end Autonomous Driving via Large Language Model](https://mlsanity.com/paper/2310.01412/) (2023)
- [Learning Interactive Real-World Simulators](https://mlsanity.com/paper/2310.06114/) (2023)
- [ChauffeurNet: Learning to Drive by Imitating the Best and Synthesizing the Worst](https://mlsanity.com/paper/1812.03079/) (2018)
- [Learning by Cheating](https://mlsanity.com/paper/1912.12294/) (2019)
- [Multi-Modal Fusion Transformer for End-to-End Autonomous Driving](https://mlsanity.com/paper/2104.09224/) (2021)

## Built on by (most cited first, 30 of 42)

- [DiffusionDrive: Truncated Diffusion Model for End-to-End Autonomous Driving](https://mlsanity.com/paper/2411.15139/) (2024)
- [3D Diffuser Actor: Policy Diffusion with 3D Scene Representations](https://mlsanity.com/paper/2402.10885/) (2024)
- [Diffusion-Based Planning for Autonomous Driving with Flexible Guidance](https://mlsanity.com/paper/2501.15564/) (2025)
- [GoalFlow: Goal-Driven Flow Matching for Multimodal Trajectories Generation in End-to-End Autonomous Driving](https://mlsanity.com/paper/2503.05689/) (2025)
- [Robust Autonomy Emerges from Self-Play](https://mlsanity.com/paper/2502.03349/) (2025)
- [Generative Trajectory Stitching through Diffusion Composition](https://mlsanity.com/paper/2503.05153/) (2025)
- [Hydra-NeXt: Robust Closed-Loop Driving with Open-Loop Training](https://mlsanity.com/paper/2503.12030/) (2025)
- [Inference-Time Enhancement of Generative Robot Policies via Predictive World Modeling](https://mlsanity.com/paper/2502.00622/) (2025)
- [3D FlowMatch Actor: Unified 3D Policy for Single- and Dual-Arm Manipulation](https://mlsanity.com/paper/2508.11002/) (2025)
- [BridgeDrive: Diffusion Bridge Policy for Closed-Loop Trajectory Planning in Autonomous Driving](https://mlsanity.com/paper/2509.23589/) (2025)
- [Diffusion Model for Planning: A Systematic Literature Review](https://mlsanity.com/paper/2408.10266/) (2024)
- [Unified Uncertainty-Aware Diffusion for Multi-Agent Trajectory Modeling](https://mlsanity.com/paper/2503.18589/) (2025)
- [VDT-Auto: End-to-end Autonomous Driving with VLM-Guided Diffusion Transformers](https://mlsanity.com/paper/2502.20108/) (2025)
- [Decoupled Diffusion Sparks Adaptive Scene Generation](https://mlsanity.com/paper/2504.10485/) (2025)
- [Planning with Adaptive World Models for Autonomous Driving](https://mlsanity.com/paper/2406.10714/) (2024)
- [DiffE2E: Rethinking End-to-End Driving with a Hybrid Action Diffusion and Supervised Policy](https://mlsanity.com/paper/2505.19516/) (2025)
- [Fine-tuning Diffusion Policies with Backpropagation Through Diffusion Timesteps](https://mlsanity.com/paper/2505.10482/) (2025)
- [Model-Based Policy Adaptation for Closed-Loop End-to-End Autonomous Driving](https://mlsanity.com/paper/2511.21584/) (2025)
- [VLMPlanner: Integrating Visual Language Models with Motion Planning](https://mlsanity.com/paper/2507.20342/) (2025)
- [D-Cubed: Latent Diffusion Trajectory Optimisation for Dexterous Deformable Manipulation](https://mlsanity.com/paper/2403.12861/) (2024)
- [Imagine-2-Drive: Leveraging High-Fidelity World Models via Multi-Modal Diffusion Policies](https://mlsanity.com/paper/2411.10171/) (2024)
- [Dynamic High-Order Control Barrier Functions with Diffuser for Safety-Critical Trajectory Planning at Signal-Free Intersections](https://mlsanity.com/paper/2412.00162/) (2024)
- [FlowDrive: moderated flow matching with data balancing for trajectory planning](https://mlsanity.com/paper/2509.21961/) (2025)
- [Perfect Prediction or Plenty of Proposals? What Matters Most in Planning for Autonomous Driving](https://mlsanity.com/paper/2510.15505/) (2025)
- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [RealDrive: Retrieval-Augmented Driving with Diffusion Models](https://mlsanity.com/paper/2505.24808/) (2025)
- [ParkDiffusion++: Ego Intention Conditioned Joint Multi-Agent Trajectory Prediction for Automated Parking using Diffusion Models](https://mlsanity.com/paper/2602.20923/) (2026)
- [Heteroscedastic Diffusion for Multi-Agent Trajectory Modeling](https://mlsanity.com/paper/2605.10717/) (2026)
- [Controllable Motion Generation via Diffusion Modal Coupling](https://mlsanity.com/paper/2503.02353/) (2025)
- [Self-Imitated Diffusion Policy for Efficient and Robust Visual Navigation](https://mlsanity.com/paper/2601.22965/) (2026)

## Abstract (arXiv)

Diffusion models excel at modeling complex and multimodal trajectory distributions for decision-making and control. Reward-gradient guided denoising has been recently proposed to generate trajectories that maximize both a differentiable reward function and the likelihood under the data distribution captured by a diffusion model. Reward-gradient guided denoising requires a differentiable reward function fitted to both clean and noised samples, limiting its applicability as a general trajectory optimizer. In this paper, we propose DiffusionES, a method that combines gradient-free optimization with trajectory denoising to optimize black-box non-differentiable objectives while staying in the data manifold. Diffusion-ES samples trajectories during evolutionary search from a diffusion model and scores them using a black-box reward function. It mutates high-scoring trajectories using a truncated diffusion process that applies a small number of noising and denoising steps, allowing for much more efficient exploration of the solution space. We show that DiffusionES achieves state-of-the-art performance on nuPlan, an established closed-loop planning benchmark for autonomous driving. Diffusion-ES outperforms existing sampling-based planners, reactive deterministic or diffusion-based policies, and reward-gradient guidance. Additionally, we show that unlike prior guidance methods, our method can optimize non-differentiable language-shaped reward functions generated by few-shot LLM prompting. When guided by a human teacher that issues instructions to follow, our method can generate novel, highly complex behaviors, such as aggressive lane weaving, which are not present in the training data. This allows us to solve the hardest nuPlan scenarios which are beyond the capabilities of existing trajectory optimization methods and driving policies.