FlowCritic: Bridging Value Estimation with Flow Matching in Reinforcement Learning

Flow Matching (FM) has recently emerged as a principled and efficient generative modeling framework for reinforcement learning (RL), enabling expressive, multimodal policy parameterizations via deterministic probability transport. Compared to diffusion-based policies that rely on stochastic denoising chains, FM uses sampling based on ordinary differential equations (ODEs), with learned velocity fields, which can substantially reduce inference latency and simplify the incorporation of RL objectives. As research in flow-based RL rapidly accelerates across offline continuous control, online fine-tuning, and foundation model alignment, the literature has become highly fragmented. In this survey, we provide a comprehensive taxonomy of flow-matching approaches in reinforcement learning. We organize the literature along two axes: the target distribution being modeled (e.g., action policies, value critics, transition dynamics) and the mechanism of RL signal integration (e.g., energy-weighted regression, flow-based policy gradients, and group relative policy optimization). Furthermore, we survey emerging frontiers such as discrete and non-Euclidean action spaces, provide a systematic comparative analysis against Gaussian and diffusion baselines, and outline critical open problems. Ultimately, this survey serves as a foundational roadmap for the next generation of generative reinforcement learning and alignment.

Recent work shows that flow matching can be effective for scalar Q-value function estimation in reinforcement learning (RL), but it remains unclear why or how this approach differs from standard critics. Contrary to conventional belief, we show that their success is not explained by distributional RL, as explicitly modeling return distributions can reduce performance. Instead, we argue that the use of integration for reading out values and dense velocity supervision at each step of this integration process for training improves TD learning via two mechanisms. First, it enables robust value prediction through test-time recovery, whereby iterative computation through integration dampens errors in early value estimates as more integration steps are performed. This recovery mechanism is absent in monolithic critics. Second, supervising the velocity field at multiple interpolant values induces more plastic feature learning within the network, allowing critics to represent non-stationary TD targets without discarding previously learned features or overfitting to individual TD targets encountered during training. We formalize these effects and validate them empirically, showing that flow-matching critics substantially outperform monolithic critics (2$\times$ in final performance and around 5$\times$ in sample efficiency) in settings where loss of plasticity poses a challenge e.g., in high-UTD online RL problems, while remaining stable during learning.

Unlike standard expected-return Reinforcement Learning (RL), Distributional RL (DRL) models the full return distribution, making it better-suited for uncertainty-aware and risk-sensitive decision-making. Conditional Flow Matching (CFM) critics have recently attracted attention for modelling continuous, multi-modal return distributions. Despite this interest, there remains a substantial metric mismatch: DRL theory relies on the distributional Bellman operator being contractive in the $p$-Wasserstein distance, yet existing CFM critics are trained with arbitrary source-target couplings, so their flow-matching losses are not Wasserstein-aligned surrogates for matching Bellman target return distributions. In this work, we address this mismatch by proposing FlowIQN, a CFM critic that sorts source and Bellman target samples within each mini-batch to approximate the monotone optimal transport coupling, replacing arbitrary pairings with quantile-aligned flow paths. We prove that the loss of our quantile-coupled CFM critic yields a Wasserstein-aligned approximate projection compatible with the foundations of DRL. To our knowledge, FlowIQN is the first flow-matching distributional critic with an explicit Wasserstein-aligned projection guarantee. We further extend FlowIQN with shortcut models for efficient inference. Empirical results show that FlowIQN improves Wasserstein return-distribution accuracy over other CFM critics. It also yields competitive performance on offline RL benchmarks across multiple policy extraction methods, providing a theoretically grounded CFM critic that is readily compatible with DRL pipelines. Code: https://github.com/ori-goals/flowIQN.