Generative policies based on expressive model classes, such as diffusion and flow matching, are well-suited to complex control problems with highly multimodal action distributions. Their expressivity, however, comes at a significant inference cost: generating each action typically requires simulating many steps of the generative process, compounding latency across sequential decision-making rollouts. We introduce flow map policies, a novel class of generative policies designed for fast action generation by learning to take arbitrary-size jumps including one-step jumps-across the generative dynamics of existing flow-based policies. We instantiate flow map policies for offline-to-online reinforcement learning (RL) and formulate online adaptation as a trust-region optimization problem that improves the critic's Q-value while remaining close to the offline policy. We theoretically derive FLOW MAP Q-GUIDANCE (FMQ), a principled closed-form learning target that is optimal for adapting offline flow map policies under a critic-guided trust-region constraint. We further introduce Q-GUIDED BEAM SEARCH (QGBS), a stochastic flow-map sampler that combines renoising with beam search to enable iterative inference-time refinement. Across 12 challenging robotic manipulation and locomotion tasks from OGBench and RoboMimic, FMQ achieves state-of-the-art performance in offline-to-online RL, outperforming the previous one-step policy MVP by a relative improvement of 21.3% on the average success rate.
Iterative generative modeling techniques, such as flow matching, provide powerful tools to model complex behaviors for effective offline reinforcement learning (RL). In this work, we propose a new off-policy RL algorithm that trains a flow policy based on prior data. Our idea starts from the "expanded" Markov decision process (MDP) framework, which treats individual flow refinement steps as separate actions in an MDP. To enable off-policy RL within this framework, we apply two techniques: we generate virtual on-policy trajectories (by "reversing" flows) to make this framework compatible with prior data, and we apply a bias-and-variance reduction technique to mitigate the curse of horizon in off-policy RL. We call the resulting algorithm Reversal Q-learning (RQL). RQL has several advantages over previous flow-based RL methods: it does not suffer from backpropagation through time, makes better use of the learned value function, and directly trains the full, expressive flow policy. Through our experiments on 50 challenging simulated robotic tasks, we show that RQL leads to the best average offline RL performance compared to state-of-the-art flow-based offline RL algorithms.
Flow-based policies offer an expressive representation for online reinforcement learning, but conventional flow matching requires samples drawn from the distribution to be modeled. This poses a challenge when the desired action distribution is defined only implicitly by a Q-function, since directly sampling actions from the resulting distribution is generally intractable. We propose Refinement-Based Flow Policy Optimization (RFPO), a novel framework for training a flow policy in online reinforcement learning by alternating between Q-guided sample refinement and self-target flow matching. RFPO first generates actions from Gaussian noise using the current flow policy and then uses a finite-step stochastic refinement procedure to move them toward an energy-based distribution induced by the Q-function. Each refined action is then paired with its corresponding initial noise sample and used as a fixed target for flow-matching training. By repeatedly refining its own outputs and learning from the resulting targets, RFPO incorporates Q-guidance into the policy without requiring direct samples from the target distribution, while retaining the capacity to represent multiple action modes. We further provide a theoretical analysis of the distributional dynamics induced by RFPO. Across six continuous-control tasks, RFPO matches or outperforms a standard Gaussian-policy baseline on almost every task. Experiments on six synthetic two-dimensional target distributions with diverse geometries demonstrate that RFPO captures complex multimodal structure without mode collapse.
Diffusion-based Q-learning has emerged as a powerful paradigm for offline reinforcement learning, but its reliance on multi-step denoising makes both training and inference computationally expensive and brittle. Recent efforts to accelerate diffusion Q-learning toward single-step action generation typically introduce auxiliary networks, policy distillation, or multi-phase training, which frequently compromise simplicity, stability, or performance. To address these limitations, we introduce Bootstrapped Flow Q-Learning (BFQ), a novel framework that enables accurate single-step action generation during both training and inference, without auxiliary networks or distillation procedures. BFQ adopts a divide-and-conquer view of the displacement vector along the flow path: it begins by learning short-range displacements that can be accurately estimated from the Flow Matching marginal velocity, and bootstraps these components to directly learn a noise-to-action mapping in a single step. This formulation eliminates multi-step denoising, resulting in a learning procedure that is substantially faster, simpler, and more robust. Extensive D4RL evaluations show that BFQ improves performance while significantly reducing computational cost compared to multi-step diffusion baselines, demonstrating that single-step action generation suffices for high-performance offline Reinforcement Learning.