# Flowing with Confidence

arXiv: https://arxiv.org/abs/2605.18472 · HTML: https://mlsanity.com/paper/2605.18472/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 37 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 28 of 28)

- [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)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [DeFoG: Discrete Flow Matching for Graph Generation](https://mlsanity.com/paper/2410.04263/) (2024)
- [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023)
- [Sampling-free Epistemic Uncertainty Estimation Using Approximated Variance Propagation](https://mlsanity.com/paper/1908.00598/) (2019)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [The statistical thermodynamics of generative diffusion models: Phase transitions, symmetry breaking and critical instability](https://mlsanity.com/paper/2310.17467/) (2023)
- [Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles](https://mlsanity.com/paper/2305.01754/) (2023)
- [Generative Uncertainty in Diffusion Models](https://mlsanity.com/paper/2502.20946/) (2025)
- [LeMat-GenBench: A Unified Evaluation Framework for Crystal Generative Models](https://mlsanity.com/paper/2512.04562/) (2025)
- [A Geometric Explanation of the Likelihood OOD Detection Paradox](https://mlsanity.com/paper/2403.18910/) (2024)
- [The Information Dynamics of Generative Diffusion](https://mlsanity.com/paper/2508.19897/) (2025)
- [BLIPs: Bayesian Learned Interatomic Potentials](https://mlsanity.com/paper/2508.14022/) (2025)
- [BARNN: A Bayesian Autoregressive and Recurrent Neural Network](https://mlsanity.com/paper/2501.18665/) (2025)

## Built on by (most cited first, 1 of 1)

- [Posterior Flow Matching](https://mlsanity.com/paper/2610.13994/) (2026)

## Abstract (arXiv)

Generative models can produce nonsensical text, unrealistic images, and unstable materials faster than simulation or human review can absorb; without per-sample confidence, trust erodes. Existing fixes run k ensembles or stochastic trajectories at k× compute, measuring variability between models, not model confidence. We propose Flow Matching with Confidence (FMwC). FMwC injects input-dependent multiplicative noise at selected layers, propagates its variance through the network in closed form, and integrates it along the ODE trajectory, yielding a per-sample confidence score at standard sampling cost. The score supports multiple uses: filtering improves image quality and thermodynamic stability of crystals; editing rewinds trajectories to the points where the model commits and redirects them; and adaptive stepping concentrates ODE compute where the flow is ambiguous. We find that the confidence score correlates with the magnitude of the divergence of the learned velocity field, which gives us a window to understand the generative process, opening up surgical forms of guidance that target the moments that matter, new sampling algorithms and interpretability of generative models.