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Diffusion Sampling Correction via Approximately 10 Parameters
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Proposes PAS, a PCA-based adaptive search that learns a handful of coordinates on top-PCA basis vectors to correct existing diffusion ODE solvers (DDIM, iPNDM) with about 10 stored parameters and sub-minute training.
Problem
Slow sampling of diffusion probabilistic models; distillation and training-based acceleration methods require large training costs and parameter storage, and can disrupt the original ODE trajectory.
Approach
Use PCA on existing sampling trajectories to get a few orthogonal basis vectors and learn only their coordinates to correct the sampling direction; an adaptive search corrects only high-curvature ("S"-shaped truncation error) steps, reducing stored parameters to roughly 10.
Key results
- On CIFAR10 with 10 NFE, DDIM + PAS reaches FID 4.37 versus 15.69 for DDIM, using 12 parameters and sub-minute training on a single A100.
- iPNDM + PAS achieves FID 2.84 on CIFAR10 at NFE=10 versus 3.69 for iPNDM.
- On Stable Diffusion v1.4 at NFE=10, DDIM + PAS obtains FID 14.23 versus 16.56 for DDIM and 15.32 for DPM-Solver-v3.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add PAS to iPNDM | iPNDM · CIFAR10 32×32, NFE=10 | FID: 3.69 -> 2.84 | Helped |
| Add PAS to iPNDM | iPNDM · FFHQ 64×64, NFE=10 | FID: 4.95 -> 4.28 | Helped |
| Add PAS to iPNDM | iPNDM · ImageNet 64×64, NFE=10 | FID: 5.64 -> 5.32 | Helped |
| Add PAS to iPNDM | iPNDM · LSUN Bedroom 256×256, NFE=10 | FID: 6.17 -> 5.14 | Helped |
| Add PAS to DDIM | DDIM · Stable Diffusion v1.4, NFE=10 | FID: 16.56 -> 14.23 | Helped |
| Remove adaptive search from PAS (ablation) | DDIM + PAS · CIFAR10 32×32, NFE=10 | FID: 4.37 -> 120.32 | Hurt |
| Remove adaptive search from PAS (ablation) | DDIM + PAS · FFHQ 64×64, NFE=10 | FID: 5.61 -> 93.62 | Hurt |
| Use the top 2 rather than 3 or 4 basis vectors (ablation) | PAS correcting DDIM · CIFAR10 | FID | Hurt |
| Increase the number of ground-truth trajectories from 500 toward 5k (ablation) | PAS correcting DDIM · CIFAR10 | FID | Helped |
| Change the solver used to generate ground-truth trajectories among Heun, DDIM, and DPM-Solver-2 (ablation) | PAS correcting DDIM · CIFAR10 and FFHQ | FID | No clear effect |
| Set tolerance τ to 10⁻¹ instead of 10⁻² (ablation) | PAS correcting DDIM · CIFAR10 32×32 | FID: 17.13 -> 49.68 | Hurt |
| Add teleportation (TP) to iPNDM + PAS | iPNDM + PAS · CIFAR10 32×32, NFE=10 | FID: 2.84 -> 2.40 | Helped |
Surprising findings
- Applying PCA correction at every step without adaptive search (PAS(-AS)) makes FID much worse than plain DDIM (e.g., 120.32 vs 15.69 at NFE=10 on CIFAR10).
- LPIPS as a training loss gave the lowest average performance, attributed to being trained on clean images.
Limitations
- Gains on DDIM are large but on stronger solvers such as iPNDM at some settings the improvement is smaller or absent (e.g., FID slightly worse at NFE=4 on FFHQ).
- Hyperparameters (learning rate, loss, tolerance) must be chosen per solver and dataset, and FID has no direct loss so loss choice is heuristic.
Experimental setup
Datasets: CIFAR10 FFHQ 64x64 ImageNet 64x64 LSUN Bedroom 256x256 MS-COCO validation
Benchmarks: CIFAR10 FFHQ 64x64 ImageNet 64x64 LSUN Bedroom 256x256 Stable Diffusion v1.4 on MS-COCO
Metrics: FID L2 L1
Baselines: DDIM DPM-Solver-2 DPM-Solver++(3M) DEIS-tAB3 UniPC(3M) iPNDM AMED GITS DPM-Solver-v3 TP
Builds on: DDIM DPM-Solver iPNDM EDM Analytic-based teleportation (Wang et al.)
Closest papers by meaning
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