# Balancing Frequencies and Pixels in Flow Matching

arXiv: https://arxiv.org/abs/2609.02748 · HTML: https://mlsanity.com/paper/2609.02748/

## Key facts

- Cited by 1 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 52 of its 69 references that are in the map.
- First posted on arXiv 2 Sep 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 52)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [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)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [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)
- [PixArt-α: Fast Training of Diffusion Transformer for Photorealistic Text-to-Image Synthesis](https://mlsanity.com/paper/2310.00426/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Scaling up GANs for Text-to-Image Synthesis](https://mlsanity.com/paper/2303.05511/) (2023)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [SANA: Efficient High-Resolution Image Synthesis with Linear Diffusion Transformers](https://mlsanity.com/paper/2410.10629/) (2024)

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

- [Beyond the Manifold Hypothesis: Hybrid Spectral Parameterizations for Flow Matching](https://mlsanity.com/paper/2609.32432/) (2026)

## Abstract (arXiv)

Natural images follow a 1/f2 spectral distribution: most signal energy lies in the low spatial frequencies, while the perceptually important structures such as textures and edges occupy sparse high-frequency bands. Pixel-space reconstruction objectives, however, treat all spatial errors uniformly, causing low frequencies to dominate the optimization signal and delaying the learning of fine-scale details. In this work, we identify this objective-level spectral imbalance as a key inefficiency in training pixel-space flow models. To address it, we propose a Focal Log-Frequency Loss (f-loss), a spectrally balanced objective that equalizes the learning signal across frequencies, emphasizing high-frequency components that are otherwise underrepresented in pixel-space objectives. Building on this, we introduce a simple training strategy that combines frequency and pixel supervision: we first emphasize frequency-domain learning early to capture all frequencies, and then transition to standard pixel-space v-loss for spatial refinement. This balancing mitigates the low-frequency bias of pixel losses and aligns the training signal with the evolving needs of the model. Our approach is conceptually simple, requires no architectural changes, and acts as a drop-in replacement for flow matching losses. Across multiple model scales, it accelerates convergence by up to 40% while consistently improving FID and perceptual fidelity.