# Exposure Bias Can Alleviate Itself via Directional and Frequency Rectification in Flow Matching

arXiv: https://arxiv.org/abs/2606.28226 · HTML: https://mlsanity.com/paper/2606.28226/

## 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 61 of its 75 references that are in the map.
- First posted on arXiv 26 Jun 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 61)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [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)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [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)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [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)
- [Sequence Level Training with Recurrent Neural Networks](https://mlsanity.com/paper/1511.06732/) (2015)
- [Mean Flows for One-step Generative Modeling](https://mlsanity.com/paper/2505.13447/) (2025)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [One Step Diffusion via Shortcut Models](https://mlsanity.com/paper/2410.12557/) (2024)
- [Generating Images with Sparse Representations](https://mlsanity.com/paper/2103.03841/) (2021)
- [Kimi-Audio Technical Report](https://mlsanity.com/paper/2504.18425/) (2025)
- [FlowEdit: Inversion-Free Text-Based Editing Using Pre-Trained Flow Models](https://mlsanity.com/paper/2412.08629/) (2024)
- [Rethinking Graph Neural Networks for Anomaly Detection](https://mlsanity.com/paper/2205.15508/) (2022)
- [On Exposure Bias, Hallucination and Domain Shift in Neural Machine Translation](https://mlsanity.com/paper/2005.03642/) (2020)

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

- [Temporal and Cross-Modal Alignment for Enhanced Audiovisual Video Captioning](https://mlsanity.com/paper/2607.01667/) (2026)
- [GeoEdit: Geometry-Aware Object Editing via Dual-Branch Denoising](https://mlsanity.com/paper/2606.30003/) (2026)
- [ReCurveflow: A Flow Matching Framework that Learns Curved Reaction Trajectories to Predict Transition State Geometries](https://mlsanity.com/paper/2608.20869/) (2026)
- [Discrete Diffusion Bridges for Spatiotemporally Aligned Image Translation and Generation](https://mlsanity.com/paper/2608.29997/) (2026)

## Abstract (arXiv)

Flow Matching (FM) has achieved remarkable generative performance, yet it suffers from exposure bias due to discrepancies between training and inference. Existing mitigation strategies typically rely on static constraints or external heuristics. In this work, we propose that exposure bias itself inherently contains dynamic signals that can guide its own rectification. To leverage this, we introduce DEFAR (DirEctional-Frequency Adaptive Rectification). This framework simulates the single-step inference process during training to identify exposure bias. It utilizes directional and frequency-adaptive feedback signals from the bias itself to enhance the model's bias tolerance. It consists of two key components: (1) Anti-Drift Rectification (ADR). ADR treats inference-time drift as a signal to learn the direction to steer deviated states back toward the target. ADR endows the model with intrinsic active self-rectification capabilities; (2) Frequency Compensation (FC). Empirically, we observe that accumulated bias often stems from a lack of low-frequency components in high-noise stages, and exposure bias carries the missing frequency. FC leverages the bias itself as a self-feedback weighting factor to reinforce the missing frequency components. Experiments on CIFAR-10, CelebA-64, and ImageNet-256/512 show that DEFAR outperforms prior baselines and further demonstrates favorable scalability, compatibility, and inference robustness.