# AdaFlow: Imitation Learning with Variance-Adaptive Flow-Based Policies

arXiv: https://arxiv.org/abs/2402.04292 · HTML: https://mlsanity.com/paper/2402.04292/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for offline RL, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 50 of its 60 references that are in the map.
- First posted on arXiv 6 Feb 2024.

## Placed in

- Offline RL and imitation learning from data / [Diffusion and flow policies for offline RL](https://mlsanity.com/offlinerl/diffusion-and-flow-policies-for-offline-rl/)

## Builds on (most cited first, 30 of 50)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Generative Adversarial Imitation Learning](https://mlsanity.com/paper/1606.03476/) (2016)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Behavioral Cloning from Observation](https://mlsanity.com/paper/1805.01954/) (2018)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)

## Built on by (most cited first, 30 of 50)

- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulation](https://mlsanity.com/paper/2412.04987/) (2024)
- [Learning Robotic Manipulation Policies from Point Clouds with Conditional Flow Matching](https://mlsanity.com/paper/2409.07343/) (2024)
- [Affordance-based Robot Manipulation with Flow Matching](https://mlsanity.com/paper/2409.01083/) (2024)
- [Can We Detect Failures Without Failure Data? Uncertainty-Aware Runtime Failure Detection for Imitation Learning Policies](https://mlsanity.com/paper/2503.08558/) (2025)
- [Failure Prediction at Runtime for Generative Robot Policies](https://mlsanity.com/paper/2510.09459/) (2025)
- [Much Ado About Noising: Dispelling the Myths of Generative Robotic Control](https://mlsanity.com/paper/2512.01809/) (2025)
- [Flow Matching Imitation Learning for Multi-Support Manipulation](https://mlsanity.com/paper/2407.12381/) (2024)
- [One-Step Flow Policy Mirror Descent](https://mlsanity.com/paper/2507.23675/) (2025)
- [IMLE Policy: Fast and Sample Efficient Visuomotor Policy Learning via Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/2502.12371/) (2025)
- [FreqPolicy: Efficient Flow-based Visuomotor Policy via Frequency Consistency](https://mlsanity.com/paper/2506.08822/) (2025)
- [Fast Flow-based Visuomotor Policies via Conditional Optimal Transport Couplings](https://mlsanity.com/paper/2505.01179/) (2025)
- [One-Step Flow Policy: Self-Distillation for Fast Visuomotor Policies](https://mlsanity.com/paper/2603.12480/) (2026)
- [Local Flow Matching Generative Models](https://mlsanity.com/paper/2410.02548/) (2024)
- [UniConFlow: A Unified Constrained Flow-Matching Framework for Certified Motion Planning](https://mlsanity.com/paper/2506.02955/) (2025)
- [Drift-Based Policy Optimization: Native One-Step Policy Learning for Online Robot Control](https://mlsanity.com/paper/2604.03540/) (2026)
- [OMP: One-step Meanflow Policy with Directional Alignment](https://mlsanity.com/paper/2512.19347/) (2025)
- [WarmPrior: Straightening Flow-Matching Policies with Temporal Priors](https://mlsanity.com/paper/2605.13959/) (2026)
- [HumanoidMimicGen: Data Generation for Loco-Manipulation via Whole-Body Planning](https://mlsanity.com/paper/2605.27724/) (2026)
- [Extremum Flow Matching for Offline Goal Conditioned Reinforcement Learning](https://mlsanity.com/paper/2505.19717/) (2025)
- [Train-Once Plan-Anywhere Kinodynamic Motion Planning via Diffusion Trees](https://mlsanity.com/paper/2508.21001/) (2025)
- [Diffusion Bridge or Flow Matching? A Unifying Framework and Comparative Analysis](https://mlsanity.com/paper/2509.24531/) (2025)
- [Sample from What You See: Visuomotor Policy Learning via Diffusion Bridge with Observation-Embedded Stochastic Differential Equation](https://mlsanity.com/paper/2512.07212/) (2025)
- [Formalizing the Sampling Design Space of Diffusion-Based Generative Models via Adaptive Solvers and Wasserstein-Bounded Timesteps](https://mlsanity.com/paper/2602.12624/) (2026)
- [ProbeFlow: Training-Free Adaptive Flow Matching for Vision-Language-Action Models](https://mlsanity.com/paper/2603.17850/) (2026)
- [Dense-Jump Flow Matching with Non-Uniform Time Scheduling for Robotic Policies: Mitigating Multi-Step Inference Degradation](https://mlsanity.com/paper/2509.13574/) (2025)
- [Boosting Maximum Entropy Reinforcement Learning via One-Step Flow Matching](https://mlsanity.com/paper/2602.01606/) (2026)
- [Ada3Drift: Adaptive Training-Time Drifting for One-Step 3D Visuomotor Robotic Manipulation](https://mlsanity.com/paper/2603.11984/) (2026)
- [Where Should Action Generation Begin? A Learnable Source Prior for Generative Robot Policies](https://mlsanity.com/paper/2606.17408/) (2026)
- [ReMoBot: Retrieval-Based Few-Shot Imitation Learning for Mobile Manipulation with Vision Foundation Models](https://mlsanity.com/paper/2408.15919/) (2024)

## Abstract (arXiv)

Diffusion-based imitation learning improves Behavioral Cloning (BC) on multi-modal decision-making, but comes at the cost of significantly slower inference due to the recursion in the diffusion process. It urges us to design efficient policy generators while keeping the ability to generate diverse actions. To address this challenge, we propose AdaFlow, an imitation learning framework based on flow-based generative modeling. AdaFlow represents the policy with state-conditioned ordinary differential equations (ODEs), which are known as probability flows. We reveal an intriguing connection between the conditional variance of their training loss and the discretization error of the ODEs. With this insight, we propose a variance-adaptive ODE solver that can adjust its step size in the inference stage, making AdaFlow an adaptive decision-maker, offering rapid inference without sacrificing diversity. Interestingly, it automatically reduces to a one-step generator when the action distribution is uni-modal. Our comprehensive empirical evaluation shows that AdaFlow achieves high performance with fast inference speed.