# DiffFNO: Diffusion Fourier Neural Operator

arXiv: https://arxiv.org/abs/2411.09911 · HTML: https://mlsanity.com/paper/2411.09911/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 59 references that are in the map.
- First posted on arXiv 15 Nov 2024.

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Exploiting Diffusion Prior for Real-World Image Super-Resolution](https://mlsanity.com/paper/2305.07015/) (2023)
- [Activating More Pixels in Image Super-Resolution Transformer](https://mlsanity.com/paper/2205.04437/) (2022)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [SRDiff: Single Image Super-Resolution with Diffusion Probabilistic Models](https://mlsanity.com/paper/2104.14951/) (2021)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.06503/) (2022)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)

## Built on by (most cited first, 13 of 13)

- [FreqPolicy: Frequency Autoregressive Visuomotor Policy with Continuous Tokens](https://mlsanity.com/paper/2506.01583/) (2025)
- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [Mechanistic Interpretability with Sparse Autoencoder Neural Operators](https://mlsanity.com/paper/2509.03738/) (2025)
- [MGHF: Multi-Granular High-Frequency Perceptual Loss for Image Super-Resolution](https://mlsanity.com/paper/2411.13548/) (2024)
- [Operator Flow Matching for Timeseries Forecasting](https://mlsanity.com/paper/2510.15101/) (2025)
- [Adaptive Physics Transformer with Fused Global-Local Attention for Subsurface Energy Systems](https://mlsanity.com/paper/2602.11208/) (2026)
- [Beyond Visual Fidelity: Benchmarking Super-Resolution Models for Large-Scale Remote Sensing Imagery via Downstream Task Integration](https://mlsanity.com/paper/2605.00310/) (2026)
- [GeoFunFlow: Geometric Function Flow Matching for Inverse Operator Learning over Complex Geometries](https://mlsanity.com/paper/2509.24117/) (2025)
- [UFO: A Domain-Unification-Free Operator Framework for Generalized Operator Learning](https://mlsanity.com/paper/2605.12700/) (2026)
- [Discontinuous Galerkin Neural Operator for Pathology Defocus Deblurring](https://mlsanity.com/paper/2605.23282/) (2026)
- [Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems](https://mlsanity.com/paper/2606.18305/) (2026)
- [Dual-Prior Guided Null-Space Learning with Mixture-of-Splines for Arbitrary Medical Slice Super-Resolution](https://mlsanity.com/paper/2606.26716/) (2026)
- [LaST-SR: Laplace-Inspired Steady-Transient Complex-Frequency Decomposition for Single Image Super-Resolution](https://mlsanity.com/paper/2609.02063/) (2026)

## Abstract (arXiv)

We introduce DiffFNO, a novel diffusion framework for arbitrary-scale super-resolution strengthened by a Weighted Fourier Neural Operator (WFNO). Mode Rebalancing in WFNO effectively captures critical frequency components, significantly improving the reconstruction of high-frequency image details that are crucial for super-resolution tasks. Gated Fusion Mechanism (GFM) adaptively complements WFNO's spectral features with spatial features from an Attention-based Neural Operator (AttnNO). This enhances the network's capability to capture both global structures and local details. Adaptive Time-Step (ATS) ODE solver, a deterministic sampling strategy, accelerates inference without sacrificing output quality by dynamically adjusting integration step sizes ATS. Extensive experiments demonstrate that DiffFNO achieves state-of-the-art (SOTA) results, outperforming existing methods across various scaling factors by a margin of 2-4 dB in PSNR, including those beyond the training distribution. It also achieves this at lower inference time. Our approach sets a new standard in super-resolution, delivering both superior accuracy and computational efficiency.