# Flow Matching with Uncertainty Quantification and Guidance

arXiv: https://arxiv.org/abs/2602.10326 · HTML: https://mlsanity.com/paper/2602.10326/

## Key facts

- Cited by 4 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 37 of its 44 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## 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 37)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [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)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [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)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023)
- [On the Pitfalls of Heteroscedastic Uncertainty Estimation with Probabilistic Neural Networks](https://mlsanity.com/paper/2203.09168/) (2022)
- [Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Models](https://mlsanity.com/paper/2410.02416/) (2024)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [Affordance-based Robot Manipulation with Flow Matching](https://mlsanity.com/paper/2409.01083/) (2024)

## Built on by (most cited first, 4 of 4)

- [Uncertainty in a Single Pass: A Closed-Form Identity for One-Step Flow Matching](https://mlsanity.com/paper/2605.00941/) (2026)
- [The Geometry of Flow-Matching Uncertainty: A Cost-free Uncertainty Proxy and Its Application in Flow-based VLA Failure Detection](https://mlsanity.com/paper/2607.27933/) (2026)
- [LM-X: Explainable Vision--Language--Action Modeling via Progress, Event, and Uncertainty Prediction](https://mlsanity.com/paper/2608.25757/) (2026)
- [Posterior Flow Matching](https://mlsanity.com/paper/2610.13994/) (2026)

## Abstract (arXiv)

Despite the remarkable success of sampling-based generative models such as flow matching, they can still produce samples of inconsistent or degraded quality. To assess sample reliability and improve sample fidelity, we propose uncertainty-aware flow matching (UA-Flow), a lightweight extension of flow matching that predicts the velocity field together with heteroscedastic uncertainty. UA-Flow estimates spatially localized sample uncertainty by propagating velocity uncertainty through the flow dynamics. The resulting estimates serve as reliability signals that reflect data-manifold support for each generated sample or region. We further use them to steer generation via uncertainty-aware guidance (UG) and uncertainty-aware classifier-free guidance (UCFG). Experiments on ImageNet and CIFAR-10 show that UA-Flow's uncertainty tracks sample fidelity more consistently than element-wise baselines and that these signals also carry information about data-manifold support. On ImageNet, UG increases precision at the cost of recall and improves FID, while UCFG maintains lower FID than CFG at large guidance scales.