Pseudo Numerical Methods for Diffusion Models on Manifolds (PNDM)

This repo is the official PyTorch implementation for the paper Pseudo Numerical Methods for Diffusion Models on Manifolds

by Luping Liu, Yi Ren, Zhijie Lin, Zhou Zhao (Zhejiang University).

What does this code do?

This code is not only the official implementation for PNDM, but also a generic framework for DDIM-like models including:

• Pseudo Numerical Methods for Diffusion Models on Manifolds (PNDM)
• Denoising Diffusion Implicit Models (DDIM)
• Score-Based Generative Modeling through Stochastic Differential Equations (PF)
• Improved Denoising Diffusion Probabilistic Models (iDDPM)

Structure

This code contains three main objects including method, schedule and model. The following table shows the options supported by this code and the role of each object.

Object	Option	Role
method	DDIM, S-PNDM, F-PNDM, FON, PF	the numerical method used to generate samples
schedule	linear, quad, cosine	the schedule of adding noise to images
model	DDIM, iDDPM, PF, PF_deep	the neural network used to fit noise

All of them can be combined at will, so this code provide at least 5x3x4=60 choices to generate samples.

How to run the code

Dependencies

Run the following to install a subset of necessary python packages for our code.

pip install -r requirements.txt

Tip: mpi4py can make the generation process faster using multi-gpus. It is not necessary and can be removed freely.

Usage

Evaluate our models through main.py.

python main.py --runner sample --method F-PNDM --sample_speed 50 --device cuda --config ddim-cifar10.yml --image_path temp/results --model_path temp/models/ddim/ema_cifar10.ckpt

• runner (train|sample): choose the mode of runner
• method (DDIM|FON|S-PNDM|F-PNDM|PF): choose the numerical methods
• sample_speed: control the total generation step
• device (cpu|cuda:0): choose the device to use
• config: choose the config file
• image_path: choose the path to save images
• model_path: choose the path of model

Train our models through main.py.

python main.py --runner train --device cuda --config ddim-cifar10.yml --train_path temp/train

• train_path: choose the path to save training status

Checkpoints & statistics

All checkpoints of models and precalculated statistics for FID are provided in this Onedrive.

References

If you find the code useful for your research, please consider citing:

@inproceedings{liu2022pseudo,
    title={Pseudo Numerical Methods for Diffusion Models on Manifolds},
    author={Luping Liu and Yi Ren and Zhijie Lin and Zhou Zhao},
    booktitle={International Conference on Learning Representations},
    year={2022},
    url={https://openreview.net/forum?id=PlKWVd2yBkY}
}

This work is built upon some previous papers which might also interest you:

• Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems 33 (2020): 6840-6851.
• Jiaming Song, Chenlin Meng, and Stefano Ermon. Denoising Diffusion Implicit Models. International Conference on Learning Representations. 2020.
• Yang Song, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-Based Generative Modeling through Stochastic Differential Equations. International Conference on Learning Representations. 2020.