# Adjoint Guidance Flow: Amortized Critic Guidance for VLA Policies

arXiv: https://arxiv.org/abs/2609.34944 · HTML: https://mlsanity.com/paper/2609.34944/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Efficient VLA inference and adaptation, one of 13 directions in Vision-language-action models.
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- Vision-language-action models / [Efficient VLA inference and adaptation](https://mlsanity.com/vla/efficient-vla-inference-and-adaptation/)

## Builds on (most cited first, 28 of 28)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [SmolVLA: A Vision-Language-Action Model for Affordable and Efficient Robotics](https://mlsanity.com/paper/2506.01844/) (2025)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [RoboCasa: Large-Scale Simulation of Everyday Tasks for Generalist Robots](https://mlsanity.com/paper/2406.02523/) (2024)
- [Deep Imitation Learning for Complex Manipulation Tasks from Virtual Reality Teleoperation](https://mlsanity.com/paper/1710.04615/) (2017)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Learning a Diffusion Model Policy from Rewards via Q-Score Matching](https://mlsanity.com/paper/2312.11752/) (2023)
- [Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images](https://mlsanity.com/paper/2106.07009/) (2021)
- [MolmoAct2: Action Reasoning Models for Real-world Deployment](https://mlsanity.com/paper/2605.02881/) (2026)
- [Q-learning with Adjoint Matching](https://mlsanity.com/paper/2601.14234/) (2026)
- [Q-Flow: Stable and Expressive Reinforcement Learning with Flow-Based Policy](https://mlsanity.com/paper/2605.13435/) (2026)
- [Test-Time Gradient Guidance of Flow Policies in Reinforcement Learning](https://mlsanity.com/paper/2606.11087/) (2026)
- [FlowDPG: Deterministic Policy Gradient on Flow Matching Policies for Real-World Manipulation](https://mlsanity.com/paper/2606.22303/) (2026)
- [Guided Action Flow: Q-Guided Inference for Flow-Matching Vision-Language-Action Policies](https://mlsanity.com/paper/2607.02092/) (2026)
- [QPILOTS: Efficient Test-Time Q-Steering for Flow Policies](https://mlsanity.com/paper/2606.14801/) (2026)

## Abstract (arXiv)

Flow-based Vision-Language-Action (VLA) policies are typically trained by behavior cloning and thus do not explicitly optimize long-term task return. Critic guidance steers generation toward higher-value actions, but existing methods differentiate the critic through a one-step surrogate of the sampler and back-propagate a critic ensemble at every flow step. In contrast, here we propose Adjoint Guidance Flow (AGF), which amortizes trajectory-aware critic guidance into a lightweight guidance network while preserving the pretrained VLA policy. Specifically, we formulate critic-guided flow generation as a deterministic optimal control problem, whose optimal guidance is a costate that carries the terminal critic gradient back through the remaining flow, and regress the guidance network onto this costate while keeping both the VLA and critic frozen. This design provides favorable memory and throughput scaling during training, and inference needs one guidance-network forward pass per step, without the critic ensemble, back-propagation, or adjoint computation. Across LIBERO, RoboCasa, and LIBERO-Pro, AGF consistently improves pretrained VLAs, remains competitive with critic-guidance and policy-fine-tuning baselines, and is the most robust method when a single guidance strength is deployed across tasks. Compared with QGF, AGF runs 3.6× faster per guidance step with 7.0× fewer parameters, with comparable and even better performance, showing that critic guidance can be trajectory-aware and lightweight.