# Show the Signal, Hide the Noise: Spectral Forcing for Pixel-Space Diffusion

arXiv: https://arxiv.org/abs/2606.15236 · HTML: https://mlsanity.com/paper/2606.15236/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 39 of its 46 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 39)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [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)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [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)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [Diffusion Transformers with Representation Autoencoders](https://mlsanity.com/paper/2510.11690/) (2025)
- [Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks](https://mlsanity.com/paper/1506.05751/) (2015)
- [Focal Frequency Loss for Image Reconstruction and Synthesis](https://mlsanity.com/paper/2012.12821/) (2020)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [PixelFlow: Pixel-Space Generative Models with Flow](https://mlsanity.com/paper/2504.07963/) (2025)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Latent Diffusion Model without Variational Autoencoder](https://mlsanity.com/paper/2510.15301/) (2025)
- [PixNerd: Pixel Neural Field Diffusion](https://mlsanity.com/paper/2507.23268/) (2025)
- [Frido: Feature Pyramid Diffusion for Complex Scene Image Synthesis](https://mlsanity.com/paper/2208.13753/) (2022)

## Built on by (most cited first, 2 of 2)

- [Persistence Forcing: Exploiting Feature Specialization in Pixel-Space Diffusion](https://mlsanity.com/paper/2609.36014/) (2026)
- [Pixel-Space Diffusion via Observation Operators](https://mlsanity.com/paper/2608.21885/) (2026)

## Abstract (arXiv)

Pixel-space diffusion models are trained on full-bandwidth noisy images, yet the useful signal available to the denoiser is strongly frequency dependent. Under rectified-flow diffusion and natural-image power-law spectra, the per-band data-to-noise contour k*(t) = (1-t)-2/α separates a signal-bearing low-frequency region from a noise-dominated high-frequency region at each time t. We show that this implicit coarse-to-fine structure is not merely descriptive: it induces a capacity-allocation problem. A standard pixel-space denoiser must discover the moving bandwidth boundary internally and can spend computation on frequency-time regions where the optimal prediction collapses to deterministic baselines rather than data-distribution modeling. To make this boundary explicit, we introduce Spectral Forcing, a parameter-free, time-conditional 2D-DCT low-pass operator applied to the noisy input before the patch embedder. Its cutoff expands monotonically with the diffusion time and becomes the identity at the data endpoint. Through controlled synthetic experiments, we identify the regime in which the operator is beneficial: coarse patch tokenization and data whose high-frequency content is predominantly noise rather than essential signal. On ImageNet-256 with JiT-700M/32, Spectral Forcing consistently improves both FID and Inception Score across different training epochs, demonstrating robust gains throughout training; at finer tokenization, the spectral forcing is still competitive. We further insert the unchanged operator into SenseNova-U1, a unified text-to-image model, where it improves DPG-Bench and GenEval, showing that the input-side spectral prior transfers beyond class-conditional generation. These results suggest a route to capacity-efficient pixel-space diffusion by showing the signal and hiding the noise.