# Flow Matching in the Low-Noise Regime: Pathologies and a Contrastive Remedy

arXiv: https://arxiv.org/abs/2509.20952 · HTML: https://mlsanity.com/paper/2509.20952/

## Key facts

- Cited by 3 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 31 of its 40 references that are in the map.
- First posted on arXiv 25 Sep 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 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Chameleon: Mixed-Modal Early-Fusion Foundation Models](https://mlsanity.com/paper/2405.09818/) (2024)
- [Janus-Pro: Unified Multimodal Understanding and Generation with Data and Model Scaling](https://mlsanity.com/paper/2501.17811/) (2025)
- [Emu3: Next-Token Prediction is All You Need](https://mlsanity.com/paper/2409.18869/) (2024)
- [Show-o: One Single Transformer to Unify Multimodal Understanding and Generation](https://mlsanity.com/paper/2408.12528/) (2024)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Janus: Decoupling Visual Encoding for Unified Multimodal Understanding and Generation](https://mlsanity.com/paper/2410.13848/) (2024)
- [Your Diffusion Model is Secretly a Zero-Shot Classifier](https://mlsanity.com/paper/2303.16203/) (2023)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [MetaMorph: Multimodal Understanding and Generation via Instruction Tuning](https://mlsanity.com/paper/2412.14164/) (2024)
- [Denoising Diffusion Autoencoders are Unified Self-supervised Learners](https://mlsanity.com/paper/2303.09769/) (2023)
- [Representation Entanglement for Generation: Training Diffusion Transformers Is Much Easier Than You Think](https://mlsanity.com/paper/2507.01467/) (2025)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Deconstructing Denoising Diffusion Models for Self-Supervised Learning](https://mlsanity.com/paper/2401.14404/) (2024)
- [Optimal algorithms for smooth and strongly convex distributed optimization in networks](https://mlsanity.com/paper/1702.08704/) (2017)
- [Diffuse and Disperse: Image Generation with Representation Regularization](https://mlsanity.com/paper/2506.09027/) (2025)
- [Generative Pre-training for Speech with Flow Matching](https://mlsanity.com/paper/2310.16338/) (2023)
- [Is Noise Conditioning Necessary for Denoising Generative Models?](https://mlsanity.com/paper/2502.13129/) (2025)
- [The Emergence of Reproducibility and Generalizability in Diffusion Models](https://mlsanity.com/paper/2310.05264/) (2023)
- [Understanding Representation Dynamics of Diffusion Models via Low-Dimensional Modeling](https://mlsanity.com/paper/2502.05743/) (2025)
- [Diffusion models under low-noise regime](https://mlsanity.com/paper/2506.07841/) (2025)
- [Conditioning Residuals for Diffusion Models via Representation Feedback](https://mlsanity.com/paper/2505.10999/) (2025)

## Built on by (most cited first, 3 of 3)

- [Self-Supervised Flow Matching for Scalable Multi-Modal Synthesis](https://mlsanity.com/paper/2603.06507/) (2026)
- [RepFlow: Reciprocal Supervision Improves Generation and Representation in Flow Models](https://mlsanity.com/paper/2609.33217/) (2026)
- [Scaling Online Optimal Transport Minibatches for Flow Matching](https://mlsanity.com/paper/2610.18838/) (2026)

## Abstract (arXiv)

Flow matching has recently emerged as a powerful alternative to diffusion models, providing a continuous-time formulation for generative modeling and representation learning. Yet, we show that this framework suffers from a fundamental instability in the low-noise regime. As noise levels approach zero, arbitrarily small perturbations in the input can induce large variations in the velocity target, causing the condition number of the learning problem to diverge. This ill-conditioning not only slows optimization but also forces the encoder to reallocate its limited Jacobian capacity toward noise directions, thereby degrading semantic representations. We provide the first theoretical analysis of this phenomenon, which we term the low-noise pathology, establishing its intrinsic link to the structure of the flow matching objective. Building on these insights, we propose Local Contrastive Flow (LCF), a hybrid training protocol that replaces direct velocity regression with contrastive feature alignment at small noise levels, while retaining standard flow matching at moderate and high noise. Empirically, LCF not only improves convergence speed but also stabilizes representation quality. Our findings highlight the critical importance of addressing low-noise pathologies to unlock the full potential of flow matching for both generation and representation learning.