Preference optimization is a standard alignment method for generative models, yet extending it to continuous-time dynamics remains non-trivial. In flow matching, reward-driven updates modify transport trajectories without an inherent constraint to the pretrained data manifold and can move terminal samples off the pretrained support. We formalize this failure mode as manifold drift. Theoretically, we show that optimal flow matching recovers the terminal data distribution, whereas a preference update leaves the pretrained manifold whenever its induced terminal displacement has a nonzero normal component. As a remedy, we propose ThermoDPO, a temperature-controlled objective that anchors pairwise preference optimization on preferred samples. Across temperature regimes, this objective connects rejection sampling fine-tuning and FlowDPO and controls a pointwise reconstruction-based surrogate for manifold distance. To counteract diminished signals at low temperatures, we further introduce a weighted variant, ThermoDPO-weighted. On the main toy benchmark, ThermoDPO-weighted attains a StrictScore of 0.899, compared with 0.629 for FlowDPO and 0.857 for FlowDPO+RFT. On SD3.5-M at CFG = 4.5, it improves OCR by 47.5% and the average of four metrics by 16.0%.
Few-step flow-map generators, such as consistency models and MeanFlow, accelerate sampling by directly learning long-range transport maps between noise and data. However, these models are typically deterministic, which makes them difficult to optimize with reinforcement learning (RL) post-training methods that require stochastic trajectories and well-defined likelihood ratios. Existing SDE-based stochasticization techniques are designed for velocity-based samplers with infinitesimal or finely discretized transitions, and therefore do not directly apply to long-range flow maps. In this work, we propose Flow-Map GRPO, an online RL post-training framework for deterministic few-step flow-map generators. The key component is Anchored Stochastic Flow Map Composition (ASFMC), a path-preserving stochasticization mechanism that introduces randomness through anchor-based conditional resampling while preserving the original marginal probability path of the deterministic flow map. We derive GRPO objectives for both single-time and two-time flow-map parameterizations. Experiments on few-step FLUX-based text-to-image generators, including MeanFlow and sCM, show that Flow-Map GRPO improves pretrained deterministic flow-map models across reward-based, perceptual, and task-level evaluation metrics. Our results demonstrate that deterministic few-step flow-map generators can be effectively aligned with RL post-training without modifying their original model parameterization or retraining them as native stochastic models.
In complex continuous-control reinforcement learning tasks, multimodal optimal actions often coincide with uncertain, multimodal return distributions, making reliable value estimation and multimodal exploration challenging. Existing value estimation methods using unimodal Gaussians restrict expressiveness and yield biased estimates. Recent generative policies can represent multimodal actions but often collapse to a few modes and under-explore high-value areas of the action space. Motivated by these challenges, we propose Dual-Flow RL, a unified actor-critic framework that jointly models a continuous return distribution and a multimodal policy distribution using conditional flow matching (CFM). This design supports reliable value estimation and sustained multimodal exploration. To further enhance exploration, we introduce an Entropy-Covariance Exploration Regulator (ECER) that enables state-aware exploration regulation leveraging policy entropy and action-uncertainty covariance. Experiments on DeepMind Control Suite and Humanoid-Bench show that Dual-Flow RL achieves state-of-the-art performance on most tasks, significantly outperforming prior diffusion-based and flow-based methods.
Aditya Oberai, Seohong Park, Sergey Levinecs.LG cs.AI
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.
Recent work has demonstrated that online reinforcement learning (RL) can substantially improve the quality and alignment of flow matching models for image and video generation. Methods such as Flow-GRPO and CPS cast the denoising process as a Markov Decision Process and apply PPO-style ratio clipping to enforce a trust region. However, we argue that ratio clipping is structurally ill-suited for flow models: the probability ratio between new and old policies is a noisy, single-sample estimate of the true policy divergence, leading to over-constraining in some regions of the trajectory and under-constraining in others. We propose Flow-DPPO (Flow Divergence Proximal Policy Optimization), which replaces ratio clipping with a divergence proximal constraint. A key observation is that the per-step policy in flow models is Gaussian, enabling exact and cheap computation of the KL divergence between old and new policies. Flow-DPPO employs an asymmetric divergence mask that blocks gradient updates only when they simultaneously move away from the trusted region and violate the divergence threshold. Experiments show that Flow-DPPO achieves higher rewards with better KL-proximal efficiency, alleviates catastrophic forgetting, promotes balanced multi-objective optimization, and enables stable multi-epoch training where ratio clipping degrades. Code and models are available at https://github.com/Tencent-Hunyuan/UniRL/tree/main/FlowDPPO.
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.