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DiffFNO: Diffusion Fourier Neural Operator
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Proposes DiffFNO, a diffusion model for arbitrary-scale super-resolution that uses a weighted Fourier neural operator with learned frequency-mode rebalancing, a gated fusion with an attention neural operator, and an adaptive-time-step ODE solver.
Problem
Arbitrary-scale image super-resolution, where standard Fourier neural operators lose high-frequency detail through mode truncation and diffusion-based SR is computationally expensive at inference.
Approach
Replaces mode truncation in FNO with a learned frequency weighting (1 + γ·||ξ||^α) that keeps all modes and emphasizes high frequencies, fuses WFNO and attention-based neural operator features with a learned spatial gate, and uses a learned non-uniform time-step schedule with an RK4 probability-flow ODE solver to cut diffusion steps from 1000 to 30.
Key results
- DiffFNO (EDSR encoder) reaches 35.72 dB PSNR at x2 and 26.48 dB at x12 on DIV2K validation, above SRNO's 34.85 and 25.91 dB.
- Adaptive time-step ODE solver reduces inference steps from 1000 to 30 (inference 141 ms vs 266 ms without ATS).
- On Set5 x2 with RDN encoder, DiffFNO reports 39.72 dB vs HiNOTE's 39.01 dB.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DiffFNO instead of HiNOTE | RDN-based arbitrary-scale super-resolution · Set5 ×2 | PSNR: 39.01 -> 39.72 | Helped |
| Use DiffFNO instead of HiNOTE | RDN-based arbitrary-scale super-resolution · Set14 ×2 | PSNR: 35.02 -> 36.01 | Helped |
| Use DiffFNO instead of HiNOTE | RDN-based arbitrary-scale super-resolution · BSD100 ×2 | PSNR: 33.02 -> 33.56 | Helped |
| Use DiffFNO instead of HiNOTE | RDN-based arbitrary-scale super-resolution · Urban100 ×8 | PSNR: 23.34 -> 23.35 | Helped |
| Add Mode Rebalancing to FNO (ablation) | WFNO on DIV2K validation · DIV2K validation ×4 | PSNR: 29.31 -> 29.70 | Helped |
| Add AttnNO and Gated Fusion Mechanism to WFNO (ablation) | WFNO on DIV2K validation · DIV2K validation ×4 | PSNR: 29.70 -> 30.40 | Helped |
| Add the full model components, including ATS ODE solver (ablation) | DiffFNO on DIV2K validation · DIV2K validation ×4 | PSNR: 30.05 -> 30.88 | Helped |
| Add AttnNO and ATS ODE solver (ablation) | DiffFNO without Mode Rebalancing on DIV2K validation · DIV2K validation ×4 | PSNR: 30.05 -> 30.46 | Helped |
| Add ATS ODE solver (ablation) | DiffFNO on DIV2K validation · DIV2K validation ×4 | Inference steps: 1000 -> 30 | Helped |
| Add ATS ODE solver (ablation) | DiffFNO on DIV2K validation · DIV2K validation ×4 | PSNR: 30.85 -> 30.88 | Helped |
Surprising findings
- The ablation shows that the diffusion process with 1000 steps is not the main source of gains in some settings: WFNO-AttnNO (no diffusion) already beats several baselines at x2-x4, and the full model's gain over it is modest at x2 (35.72 vs 35.40 dB).
Limitations
- Training and hardware details (optimizer, epochs, GPUs) are not reported in the text.
- Some reported numbers across tables are inconsistent (e.g., DiffFNO's SSIM and Table 1 vs Table 3 values), and no code is released.
Experimental setup
Datasets: DIV2K
Benchmarks: DIV2K validation Set5 Set14 BSD100 Urban100
Metrics: PSNR SSIM inference time (ms)
Baselines: Meta-SR LIIF LTE LIT LMI SRNO HiNOTE FNO
Builds on: Fourier Neural Operator SRNO DPM-Solver EDSR RDN
Closest papers by meaning
- $\infty$-Diff: Infinite Resolution Diffusion with Subsampled Mollified States (ICLR 2024 · similarity 0.88)
- Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution (ICML 2024 · similarity 0.88)
- ResDiff: Combining CNN and Diffusion Model for Image Super-resolution (AAAI 2024 · similarity 0.88)
- Effective Diffusion Transformer Architecture for Image Super-Resolution (AAAI 2025 · similarity 0.88)
- FAM Diffusion: Frequency and Attention Modulation for High-Resolution Image Generation with Stable Diffusion (CVPR 2025 · similarity 0.88)
- SinSR: Diffusion-Based Image Super-Resolution in a Single Step (CVPR 2024 · similarity 0.87)
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