Accelerating Score-based Generative Models with Preconditioned Diffusion Sampling

Paper

Accelerating Score-based Generative Models with Preconditioned Diffusion Sampling,
Hengyuan Ma, Li Zhang, Xiatian Zhu, and Jianfeng Feng
ECCV 2022

News

[2022/07/04]: PDS is accepted by ECCV 2022!

Abstract

Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their inference is very slow due to a need for many (e.g., 2000) iterations of sequential computations. An intuitive acceleration method is to reduce the sampling iterations which however causes severe performance degradation. We investigate this problem by viewing the diffusion sampling process as a Metropolis adjusted Langevin algorithm, which helps reveal the underlying cause to be ill-conditioned curvature. Under this insight, we propose a model-agnostic preconditioned diffusion sampling (PDS) method that leverages matrix preconditioning to alleviate the aforementioned problem. Crucially, PDS is proven theoretically to converge to the original target distribution of a SGM, no need for retraining. Extensive experiments on three image datasets with a variety of resolutions and diversity validate that PDS consistently accelerates off-the-shelf SGMs whilst maintaining the synthesis quality. In particular, PDS can accelerate by up to 29x on more challenging high resolution (1024x1024) image generation.

Demo

FFHQ facial images (1024x1024) generated by vanilla NCSN++ using 2000, 200, 133, 100 and 66 sampling iterations (from left to right).

FFHQ facial images (1024x1024) generated by NCSN++ w/ PDS using 2000, 200, 133, 100 and 66 sampling iterations (from left to right).

Preconditioned diffusion sampling

The Langevin dynamics applied by vanilla SGMs for generating samples is

To accelerate the convergence while keeping the steady state distribution, our PDS use the following preconditioned Langevin dynamics

where the preconditioning matrix M can be constructed by priori knowledge from the target dataset in frequency domain or space (pixel) domain, S can be any skew-symmetric matrix.

Running the Experiments

Sampling using PDS through main.py.

$ python main.py --config: Model configuration. (default: 'None')
                 --workdir: Working directory. (default: 'None')
                 --eval_folder: Output directory. (default: 'eval')
                 --speed_up: Speedup ratio. 
                 --freq_mask_path: Path to the frequency filter. (default: 'None')
                 --space_mask_path: Path to the space filter. (default: 'None') 
                 --alpha: The setting of the parameter alpha. (default: 5)

config is the path to the config file provided in configs/.
workdir is the path that stores checkpoints and samples. Pretrained checkpoints should be stored in workdir/checkpoints/ before sampling. Please download the checkpoints here.
eval_folder is the name of a subfolder in workdir for storing samples.
speed_up is the ratio (float) that the sampling process is accelerated, compared to the original one. If it is set to 20, the sampling iterations will shrink 20 times, and every step size will increase up to 20 times. The settings of sampling iterations and step size can be found in config files.
freq_mask_path and space_mask_path are the paths to the calculated frequency and space filters. We provide precalculated filters here.
alpha is the setting of the parameter that normalize the frequency filter.

Example: sampling FFHQ (1024x1024) dataset with both frequency and space filter, under 30 times acceleration.

$ python main.py --config ./configs/ve/ffhq_ncsnpp_continuous.py --workdir  yourworkdir --speed_up 30 --freq_mask_path ./ffhq_freq.npy --space_mask_path ./ffhq_space.npy

Example: sampling LSUN bedroom (256x256) dataset with only frequency filter, under 12 times acceleration.

$ python main.py --config ./configs/ve/bedroom_ncsnpp_continuous.py --workdir  yourworkdir --speed_up 12 --freq_mask_path ./bedroom_freq.npy

License

MIT

Reference

@inproceedings{ma2022pds,
  title={Accelerating Score-based Generative Models with Preconditioned Diffusion Sampling},
  author={Ma, Hengyuan and Zhang, Li and Zhu, Xiatian and Feng, Jianfeng},
  booktitle={European Conference on Computer Vision},
  year={2022}
}

Acknowledgement

Thanks to previous open-sourced repo: NCSN++

fudan-zvg/PDS