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On Accelerating Diffusion-Based Sampling Processes via Improved Integration Approximation
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Proposes improved integration approximation (IIA), which fits per-step coefficients of EDM, DDIM and DPM-Solver samplers by least squares against fine-grained solver integrations, improving FID at small NFE without changing the pre-trained model.
Problem
ODE-based diffusion samplers use pre-determined coefficients, which are inaccurate integration approximations when the number of function evaluations (NFE) is small.
Approach
Learn the per-timestep stepsizes (coefficients) of EDM, DDIM and DPM-Solver by minimizing an MSE between the coarse update and a fine-grained integration computed with the same solver over sub-steps; the quadratic problem is solved once on a small batch of initial noises and the coefficients are stored for reuse.
Key results
- On text-to-image with StableDiffusion V2 at 10 NFEs, IIA-DDIM achieves FID 13.21 versus 14.78 for DDIM (per the table, with the mapping of columns partly garbled).
- IIA-EDM consistently outperforms EDM in FID when NFE is below 25 across four pre-trained EDM models, with IIA-EDM having the smallest residual error for each NFE.
- IIA-EDM sampling time is essentially identical to EDM (e.g., 12.4s vs 12.6s per mini-batch on an RTX 2080Ti), and MMSE overhead is 42.8 to 102.1 seconds.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add MMSE-optimized integration coefficients to EDM | EDM · CIFAR10, FFHQ, AFHQV2, and ImageNet64 at fewer than 25 NFEs | FID | Helped |
| Replace the basic EDM coefficient adjustment with coefficients exploiting the internal structure of the EDM update (ablation) | BIIA-EDM · CIFAR10, FFHQ, AFHQV2, and ImageNet64 at fewer than 25 NFEs | FID | Helped |
| Use historical gradients in BIIA-EDM (ablation) | EDM · ImageNet64, greater than 25 NFEs | FID | Hurt |
| Add MMSE-optimized coefficients to DDIM | DDIM · COCO2014 validation, StableDiffusion V2, 10 NFEs | FID: 14.78 -> 13.21 | Helped |
| Add MMSE-optimized coefficients to DPM-Solver | DPM-Solver · COCO2014 validation, StableDiffusion V2, 10 NFEs | FID: 15.82 -> 12.97 | Helped |
| Add MMSE-optimized coefficients to DDIM | DDIM · COCO2014 validation, StableDiffusion V2, 30 NFEs | FID: 15.08 -> 14.03 | Helped |
| Add MMSE-optimized coefficients to DPM-Solver | DPM-Solver · COCO2014 validation, StableDiffusion V2, 30 NFEs | FID: 14.23 -> 13.26 | Helped |
| Add MMSE-optimized coefficients to conventional DDIM | DDIM · CIFAR10, LSUN bedroom, and LSUN church | FID | Helped |
| Add MMSE-optimized coefficients to SPNDM and IPNDM | SPNDM and IPNDM · Certain pre-trained models | sampling performance | Helped |
Surprising findings
- BIIA-EDM performs slightly worse than EDM on ImageNet64 when NFE exceeds 25, suggesting more accurate integration does not always improve FID at large NFE.
- DPM-Solver and PLMS have larger FID than DDIM at 10 NFEs for classifier-free guided text-to-image sampling.
Limitations
- Gains are reported mainly for small NFE (under 25); benefit at large NFE is absent or negative.
- Coefficients are fitted per pre-trained model and fixed timestep schedule, so they must be recomputed for new models or schedules.
- Text-to-image results rely on only 20 text prompts for fitting the coefficients and the paper's tables are partly garbled.
Experimental setup
Datasets: CIFAR10 FFHQ AFHQv2 ImageNet64 LSUN bedroom LSUN church COCO2014 validation
Benchmarks: CIFAR10 FFHQ AFHQv2 ImageNet64 LSUN bedroom LSUN church COCO2014
Metrics: FID CLIP score average residual error
Baselines: EDM DDIM DPM-Solver PLMS BIIA-EDM SPNDM IPNDM
Builds on: EDM DDIM DPM-Solver PNDM improved Euler method
Closest papers by meaning
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- Fast ODE-based Sampling for Diffusion Models in Around 5 Steps (CVPR 2024 · similarity 0.90)
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