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Boosting Diffusion Models with Moving Average Sampling in Frequency Domain
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Proposes MASF, a training-free sampler that applies moving averages to estimated clean samples x0 in the wavelet frequency domain with a dynamic low/high-frequency weighting, improving FID across DDIM, DDPM, DPM-Solver++, UniPC and F-PNDM.
Problem
Denoising instability in diffusion sampling: each step depends only on the current sample, so discretization errors accumulate and sampling needs many steps to converge.
Approach
Treat the iterative denoising as model optimization and apply a moving average to the estimated clean samples x0 (not the noisy xt), performed separately on Haar wavelet subbands with a frequency-dependent weighting that favors low frequencies early and high frequencies late.
Key results
- On ImageNet 64x64 with DDIM at NFE 10, FID drops from 52.19 to 22.63 with MASF.
- On MS-COCO text-conditional generation with DDIM at NFE 10, FID improves from 35.10 to 25.67.
- MASF adds roughly 0.97% extra computational cost to the sampling process, per the authors.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add MASF to DDIM | ADM · ImageNet 64 | FID: 52.19 -> 22.63 | Helped |
| Add MASF to DDIM | ADM · ImageNet 128 | FID: 20.36 -> 17.19 | Helped |
| Add MASF to DDIM | ADM · ImageNet 256 | FID: 25.68 -> 22.64 | Helped |
| Add MASF to DDIM | U-ViT · MS-COCO val | FID: 35.10 -> 25.67 | Helped |
| Add MASF to DPM-Solver++ (3Fast) | U-ViT · MS-COCO val | FID: 5.76 -> 5.69 | Helped |
| Add MASF to DDIM | ADM · LSUN Horse | FID: 18.41 -> 16.07 | Helped |
| Add MASF to DDIM | ADM · LSUN Bedroom | FID: 4.11 -> 3.76 | Helped |
| Add MASF to DDIM | ADM · LSUN Cat | FID: 12.42 -> 11.65 | Helped |
| Add MASF to DDIM | Latent DPM · FFHQ | FID: 11.92 -> 10.10 | Helped |
| Add pixel-space moving average (ablation) | DDIM · ImageNet 128×128 | FID: 23.00 -> 21.88 | Helped |
| Add frequency-domain transformation to moving average (ablation) | +MA · ImageNet 128×128 | FID: 21.88 -> 21.76 | Helped |
| Use linear adaptive weight instead of constant weight (ablation) | MASF · ImageNet 128×128 | FID: 22.05 -> 21.76 | Helped |
Surprising findings
- Applying moving average directly to noisy intermediate samples xt harms trajectories, so mapping to x0 before averaging is necessary.
- Gains are largest at small NFE, where instability is most severe.
Limitations
- Gains are smaller at higher NFE and for strong solvers (e.g., DPM-Solver++ at 25 NFE improves only 0.07 FID on MS-COCO).
- Frequency weighting schedules were hand-chosen with specific linear ranges, and hyperparameter gamma was tuned empirically.
- Evaluated only with FID; no human or other quality metrics reported.
Experimental setup
Datasets: ImageNet LSUN FFHQ MS-COCO
Benchmarks: ImageNet 64/128/256 MS-COCO LSUN Horse/Bedroom/Cat FFHQ
Metrics: FID
Baselines: DDIM DDPM DPM-Solver++ UniPC F-PNDM Spectral Diffusion
Builds on: DDIM DDPM DPM-Solver++ UniPC classifier guidance
Closest papers by meaning
- Spectral Progressive Diffusion for Efficient Image and Video Generation (NeurIPS 2026 · similarity 0.90)
- A Simple Early Exiting Framework for Accelerated Sampling in Diffusion Models (ICML 2024 · similarity 0.90)
- On the Trajectory Regularity of ODE-based Diffusion Sampling (ICML 2024 · similarity 0.89)
- Denoising Diffusion Bridge Models (ICLR 2024 · similarity 0.89)
- FAM Diffusion: Frequency and Attention Modulation for High-Resolution Image Generation with Stable Diffusion (CVPR 2025 · similarity 0.89)
- Diffusion Models With Learned Adaptive Noise (NeurIPS 2024 · similarity 0.89)
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