# A Fourier Space Perspective on Diffusion Models

arXiv: https://arxiv.org/abs/2505.11278 · HTML: https://mlsanity.com/paper/2505.11278/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 34 of its 50 references that are in the map.
- First posted on arXiv 16 May 2025.

## Placed in

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

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (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)
- [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)
- [The Kinetics Human Action Video Dataset](https://mlsanity.com/paper/1705.06950/) (2017)
- [Imagen Video: High Definition Video Generation with Diffusion Models](https://mlsanity.com/paper/2210.02303/) (2022)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [WorldSimBench: Towards Video Generation Models as World Simulators](https://mlsanity.com/paper/2410.18072/) (2024)
- [Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions](https://mlsanity.com/paper/2209.11215/) (2022)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [Rethinking FID: Towards a Better Evaluation Metric for Image Generation](https://mlsanity.com/paper/2401.09603/) (2023)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Generative Modelling With Inverse Heat Dissipation](https://mlsanity.com/paper/2206.13397/) (2022)
- [Fourier Spectrum Discrepancies in Deep Network Generated Images](https://mlsanity.com/paper/1911.06465/) (2019)
- [Low-Light Image Enhancement with Wavelet-based Diffusion Models](https://mlsanity.com/paper/2306.00306/) (2023)
- [Diffusion Probabilistic Model Made Slim](https://mlsanity.com/paper/2211.17106/) (2022)
- [Wavelet Diffusion Models are fast and scalable Image Generators](https://mlsanity.com/paper/2211.16152/) (2022)
- [Rolling Diffusion Models](https://mlsanity.com/paper/2402.09470/) (2024)
- [MatterGen: a generative model for inorganic materials design](https://mlsanity.com/paper/2312.03687/) (2023)
- [Wavelet Score-Based Generative Modeling](https://mlsanity.com/paper/2208.05003/) (2022)
- [Towards Understanding the Working Mechanism of Text-to-Image Diffusion Model](https://mlsanity.com/paper/2405.15330/) (2024)
- [WaveDM: Wavelet-Based Diffusion Models for Image Restoration](https://mlsanity.com/paper/2305.13819/) (2023)
- [Time Series Diffusion in the Frequency Domain](https://mlsanity.com/paper/2402.05933/) (2024)
- [On Error Propagation of Diffusion Models](https://mlsanity.com/paper/2308.05021/) (2023)
- [A Unified Framework for U-Net Design and Analysis](https://mlsanity.com/paper/2305.19638/) (2023)
- [Spectral Diffusion Processes](https://mlsanity.com/paper/2209.14125/) (2022)
- [Score-based Denoising Diffusion with Non-Isotropic Gaussian Noise Models](https://mlsanity.com/paper/2210.12254/) (2022)
- [Frequency Compensated Diffusion Model for Real-scene Dehazing](https://mlsanity.com/paper/2308.10510/) (2023)

## Built on by (most cited first, 30 of 52)

- [End-to-End Training for Autoregressive Video Diffusion via Self-Resampling](https://mlsanity.com/paper/2512.15702/) (2025)
- [Self-Supervised Flow Matching for Scalable Multi-Modal Synthesis](https://mlsanity.com/paper/2603.06507/) (2026)
- [Scaling Atomistic Protein Binder Design with Generative Pretraining and Test-Time Compute](https://mlsanity.com/paper/2603.27950/) (2026)
- [SeaCache: Spectral-Evolution-Aware Cache for Accelerating Diffusion Models](https://mlsanity.com/paper/2602.18993/) (2026)
- [Toward Diffusible High-Dimensional Latent Spaces: A Frequency Perspective](https://mlsanity.com/paper/2511.22249/) (2025)
- [Spectrum Matching: a Unified Perspective for Superior Diffusability in Latent Diffusion](https://mlsanity.com/paper/2603.14645/) (2026)
- [NeuralRemaster: Phase-Preserving Diffusion for Structure-Aligned Generation](https://mlsanity.com/paper/2512.05106/) (2025)
- [VFMF: World Modeling by Forecasting Vision Foundation Model Features](https://mlsanity.com/paper/2512.11225/) (2025)
- [Spectrally-Guided Diffusion Noise Schedules](https://mlsanity.com/paper/2603.19222/) (2026)
- [SerpentFlow: Generative Unpaired Domain Alignment via Shared-Structure Decomposition](https://mlsanity.com/paper/2601.01979/) (2026)
- [PyramidalWan: On Making Pretrained Video Model Pyramidal for Efficient Inference](https://mlsanity.com/paper/2601.04792/) (2026)
- [Hyper-DP3: Frequency-Aware Right-Sizing of 3D Diffusion Policies for Visuomotor Control](https://mlsanity.com/paper/2605.01581/) (2026)
- [FREPix: Frequency-Heterogeneous Flow Matching for Pixel-Space Image Generation](https://mlsanity.com/paper/2605.06421/) (2026)
- [WaiT for the Signal: Simple Frequency-Aware Flow-Matching](https://mlsanity.com/paper/2607.28760/) (2026)
- [FRAMER: Frequency-Aligned Self-Distillation with Adaptive Modulation Leveraging Diffusion Priors for Real-World Image Super-Resolution](https://mlsanity.com/paper/2512.01390/) (2025)
- [Frequency-Guided Action Diffusion via Sub-Frequency Manifold Traversal](https://mlsanity.com/paper/2605.27919/) (2026)
- [Colored Noise Diffusion Sampling](https://mlsanity.com/paper/2605.30332/) (2026)
- [Functional MRI Time Series Generation via Wavelet-Based Image Transform and Spectral Flow Matching for Brain Disorder Identification](https://mlsanity.com/paper/2605.30387/) (2026)
- [Enhancing Membership Inference Attacks on Diffusion Models from a Frequency-Domain Perspective](https://mlsanity.com/paper/2505.20955/) (2025)
- [GAGA: Gaussianity-Aware Gaussian Approximation for Efficient 3D Molecular Generation](https://mlsanity.com/paper/2507.09043/) (2025)
- [Squeezed Diffusion Models](https://mlsanity.com/paper/2508.14871/) (2025)
- [Accelerating Frequency Domain Diffusion Models with Error-Feedback Event-Driven Caching](https://mlsanity.com/paper/2604.22901/) (2026)
- [The Learnability Gap in Medical Latent Diffusion](https://mlsanity.com/paper/2605.17087/) (2026)
- [Everything at Every Scale: Scale-Invariant Diffusion with Continuous Super-Resolution](https://mlsanity.com/paper/2605.26032/) (2026)
- [HyFAD: Hybrid Time-Frequency Diffusion with Frequency-Aware Embedding for Time Series Imputation](https://mlsanity.com/paper/2606.05239/) (2026)
- [Manifold-Constrained Noise Optimization for Diverse Diffusion Sampling](https://mlsanity.com/paper/2607.23937/) (2026)
- [Cloud Diffusion Part 1: Theory and Motivation](https://mlsanity.com/paper/2507.05496/) (2025)
- [Novel View Synthesis using DDIM Inversion](https://mlsanity.com/paper/2508.10688/) (2025)
- [Perceptually Aligning Representations of Music via Noise-Augmented Autoencoders](https://mlsanity.com/paper/2511.05350/) (2025)
- [Diffusion-Inversion-Net (DIN): An End-to-End Direct Probabilistic Framework for Characterizing Hydraulic Conductivities and Quantifying Uncertainty](https://mlsanity.com/paper/2511.16926/) (2025)

## Abstract (arXiv)

Diffusion models are state-of-the-art generative models on data modalities such as images, audio, proteins and materials. These modalities share the property of exponentially decaying variance and magnitude in the Fourier domain. Under the standard Denoising Diffusion Probabilistic Models (DDPM) forward process of additive white noise, this property results in high-frequency components being corrupted faster and earlier in terms of their Signal-to-Noise Ratio (SNR) than low-frequency ones. The reverse process then generates low-frequency information before high-frequency details. In this work, we study the inductive bias of the forward process of diffusion models in Fourier space. We theoretically analyse and empirically demonstrate that the faster noising of high-frequency components in DDPM results in violations of the normality assumption in the reverse process. Our experiments show that this leads to degraded generation quality of high-frequency components. We then study an alternate forward process in Fourier space which corrupts all frequencies at the same rate, removing the typical frequency hierarchy during generation, and demonstrate marked performance improvements on datasets where high frequencies are primary, while performing on par with DDPM on standard imaging benchmarks.