# On the Guidance of Flow Matching

arXiv: https://arxiv.org/abs/2502.02150 · HTML: https://mlsanity.com/paper/2502.02150/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 36 of its 46 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 30 of 36)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [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)
- [D4RL: Datasets for Deep Data-Driven Reinforcement Learning](https://mlsanity.com/paper/2004.07219/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Riemannian Continuous Normalizing Flows](https://mlsanity.com/paper/2006.10605/) (2020)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [Training-free Linear Image Inverses via Flows](https://mlsanity.com/paper/2310.04432/) (2023)
- [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024)
- [Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.03024/) (2024)

## Built on by (most cited first, 30 of 45)

- [Diamond Maps: Efficient Reward Alignment via Stochastic Flow Maps](https://mlsanity.com/paper/2602.05993/) (2026)
- [GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models](https://mlsanity.com/paper/2509.25170/) (2025)
- [Source-Guided Flow Matching](https://mlsanity.com/paper/2508.14807/) (2025)
- [Flow Matching for Efficient and Scalable Data Assimilation](https://mlsanity.com/paper/2508.13313/) (2025)
- [SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions](https://mlsanity.com/paper/2509.24243/) (2025)
- [HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimization](https://mlsanity.com/paper/2511.08425/) (2025)
- [ARFlow: Human Action-Reaction Flow Matching with Physical Guidance](https://mlsanity.com/paper/2503.16973/) (2025)
- [Discrete Guidance Matching: Exact Guidance for Discrete Flow Matching](https://mlsanity.com/paper/2509.21912/) (2025)
- [Good Things Come in Pairs: Paired Autoencoders for Inverse Problems](https://mlsanity.com/paper/2505.06549/) (2025)
- [Posterior Inference in Latent Space for Scalable Constrained Black-box Optimization](https://mlsanity.com/paper/2507.00480/) (2025)
- [Optimization and Generation in Aerodynamics Inverse Design](https://mlsanity.com/paper/2602.03582/) (2026)
- [Astra: Toward General-Purpose Mobile Robots via Hierarchical Multimodal Learning](https://mlsanity.com/paper/2506.06205/) (2025)
- [FlowDrive: moderated flow matching with data balancing for trajectory planning](https://mlsanity.com/paper/2509.21961/) (2025)
- [SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning](https://mlsanity.com/paper/2511.05355/) (2025)
- [Implicit Maximum Likelihood Estimation for Real-time Generative Model Predictive Control](https://mlsanity.com/paper/2603.13733/) (2026)
- [On The Hidden Biases of Flow Matching Samplers](https://mlsanity.com/paper/2512.16768/) (2025)
- [GuidedBridge: Training-freely Improving Bridge Models with Prior Guidance](https://mlsanity.com/paper/2606.03119/) (2026)
- [LatentFlow: A General Framework for Conditioning Stochastic Processes](https://mlsanity.com/paper/2607.12922/) (2026)
- [STEP-OPD: Rethinking Output Targets and Internal Dynamics in On-Policy Distillation for Diffusion Models](https://mlsanity.com/paper/2608.04887/) (2026)
- [FreqFlow: Long-term forecasting using lightweight flow matching](https://mlsanity.com/paper/2511.16426/) (2025)
- [Object Reconstruction under Occlusion with Generative Priors and Contact-induced Constraints](https://mlsanity.com/paper/2512.05079/) (2025)
- [EFF-Grasp: Energy-Field Flow Matching for Physics-Aware Dexterous Grasp Generation](https://mlsanity.com/paper/2603.16151/) (2026)
- [PrismFlow: Residual Dynamics for Flow Matching in Time-Series Generation](https://mlsanity.com/paper/2605.28867/) (2026)
- [TraceFlow: Guiding Frozen Flow-Matching Robot Policies with Success and Failure Traces](https://mlsanity.com/paper/2609.20646/) (2026)
- [Controllable Flow Matching for Online Reinforcement Learning](https://mlsanity.com/paper/2511.06816/) (2025)
- [Contact Wasserstein Geodesics for Non-Conservative Schr"odinger Bridges](https://mlsanity.com/paper/2511.06856/) (2025)
- [Energy-Guided Generative Modeling for Low-Energy Molecular Structure Discovery](https://mlsanity.com/paper/2512.22597/) (2025)
- [Guided Streaming Stochastic Interpolant Policy](https://mlsanity.com/paper/2605.10051/) (2026)
- [Follow the Mean: Reference-Guided Flow Matching](https://mlsanity.com/paper/2605.10302/) (2026)
- [Conflict-Aware Additive Guidance for Flow Models under Compositional Rewards](https://mlsanity.com/paper/2605.20758/) (2026)

## Abstract (arXiv)

Flow matching has shown state-of-the-art performance in various generative tasks, ranging from image generation to decision-making, where generation under energy guidance (abbreviated as guidance in the following) is pivotal. However, the guidance of flow matching is more general than and thus substantially different from that of its predecessor, diffusion models. Therefore, the challenge in guidance for general flow matching remains largely underexplored. In this paper, we propose the first framework of general guidance for flow matching. From this framework, we derive a family of guidance techniques that can be applied to general flow matching. These include a new training-free asymptotically exact guidance, novel training losses for training-based guidance, and two classes of approximate guidance that cover classical gradient guidance methods as special cases. We theoretically investigate these different methods to give a practical guideline for choosing suitable methods in different scenarios. Experiments on synthetic datasets, image inverse problems, and offline reinforcement learning demonstrate the effectiveness of our proposed guidance methods and verify the correctness of our flow matching guidance framework. Code to reproduce the experiments can be found at https://github.com/AI4Science-WestlakeU/flow_guidance.