# Lagrangian Perturbation Diffusion Steering: Latent Reinforcement Learning for Generative Policies

arXiv: https://arxiv.org/abs/2606.01151 · HTML: https://mlsanity.com/paper/2606.01151/

## Key facts

- Cited by 4 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 34 references that are in the map.
- First posted on arXiv 31 May 2026.

## 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 robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [Offline Reinforcement Learning with Implicit Q-Learning](https://mlsanity.com/paper/2110.06169/) (2021)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations](https://mlsanity.com/paper/1709.10087/) (2017)
- [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)
- [IDQL: Implicit Q-Learning as an Actor-Critic Method with Diffusion Policies](https://mlsanity.com/paper/2304.10573/) (2023)
- [Imitating Human Behaviour with Diffusion Models](https://mlsanity.com/paper/2301.10677/) (2023)
- [NoMaD: Goal Masked Diffusion Policies for Navigation and Exploration](https://mlsanity.com/paper/2310.07896/) (2023)
- [Offline Reinforcement Learning via High-Fidelity Generative Behavior Modeling](https://mlsanity.com/paper/2209.14548/) (2022)
- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [Parrot: Data-Driven Behavioral Priors for Reinforcement Learning](https://mlsanity.com/paper/2011.10024/) (2020)
- [ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimization](https://mlsanity.com/paper/2406.04312/) (2024)
- [Towards Diverse Behaviors: A Benchmark for Imitation Learning with Human Demonstrations](https://mlsanity.com/paper/2402.14606/) (2024)
- [JUICER: Data-Efficient Imitation Learning for Robotic Assembly](https://mlsanity.com/paper/2404.03729/) (2024)
- [Noise Hypernetworks: Amortizing Test-Time Compute in Diffusion Models](https://mlsanity.com/paper/2508.09968/) (2025)
- [DiWA: Diffusion Policy Adaptation with World Models](https://mlsanity.com/paper/2508.03645/) (2025)
- [The Lottery Ticket Hypothesis in Denoising: Towards Semantic-Driven Initialization](https://mlsanity.com/paper/2312.08872/) (2023)
- [Outsourced diffusion sampling: Efficient posterior inference in latent spaces of generative models](https://mlsanity.com/paper/2502.06999/) (2025)
- [Stable-BC: Controlling Covariate Shift with Stable Behavior Cloning](https://mlsanity.com/paper/2408.06246/) (2024)

## Built on by (most cited first, 4 of 4)

- [RLMM-Flow: A Flow-based Mobile Manipulation Framework with Latent-Space Reinforcement Learning](https://mlsanity.com/paper/2607.26460/) (2026)
- [Principal Steering Subspaces for Online Adaptation of Frozen Generative Robot Policies](https://mlsanity.com/paper/2609.33765/) (2026)
- [Reachability-Aware Diffusion Policy Optimization](https://mlsanity.com/paper/2610.05969/) (2026)
- [LeWAM: A JEPA World Action Model with Diffusion-Steering-Based MPC](https://mlsanity.com/paper/2610.12407/) (2026)

## Abstract (arXiv)

Behavior cloning with high-capacity generative policies achieves strong imitation performance, but is often limited by demonstration coverage and distribution shift. Direct reinforcement learning fine-tuning can improve performance, but updating large action decoders is frequently unstable and sample inefficient. We propose Lagrangian Perturbation Diffusion Steering (LP-DS), a lightweight adaptation method that improves a frozen generative policy by learning a compact noise-space perturbation before decoding. LP-DS optimizes this perturbation with a Lagrangian trust-region objective, improving downstream value while constraining deviation from the latent prior. Across RoboMimic manipulation, OpenAI Gym locomotion, and Adroit dexterous manipulation benchmarks, LP-DS improves sample efficiency, success, and return while maintaining higher action-space entropy than unconstrained noise-space steering, with return improvements of up to 25% over prior baselines. Additional evaluations with flow-matching backbones, a large vision-language-action model, and physical Franka deployment show that LP-DS is not limited to compact diffusion policies or simulated benchmarks. Project page: https://sites.google.com/view/lp-ds/home.