# Fast Sampling of Diffusion Models with Exponential Integrator

**Authors:** Qinsheng Zhang, Yongxin Chen  
**arXiv:** [2204.13902](https://arxiv.org/abs/2204.13902)  
**Date:** 2022-04-29  
**Summary page:** https://www.summarizepaper.com/en/paper/2204.13902v1/

## Key points

- Deep models (DMs) are popular for generating high-fidelity samples in generative modeling tasks
- Drawback of DMs is slow sampling procedure requiring hundreds to thousands of time discretization steps
- Researchers Zhang and Chen developed DEIS method for fast sampling in DMs with fewer steps while maintaining high sample quality
- DEIS method leverages Exponential Integrator technique to reduce discretization errors based on diffusion process structure
- DEIS method demonstrated capability to generate high-fidelity samples in as few as 10 steps
- Experimental trials showed DEIS method took approximately 3 minutes on a single A6000 GPU to produce 50k images from CIFAR10 dataset
- By using pre-trained DMs, researchers achieved state-of-the-art sampling performance with impressive results such as 3.37 FID and 9.74 Inception score with only 15 NFEs on CIFAR10

## Summary

In recent years,  have gained significant traction for their ability to generate high-fidelity samples in generative modeling tasks. However, a major drawback of DMs is their slow sampling procedure. This typically involves hundreds to thousands of time discretization steps to achieve the desired accuracy. In response to this limitation, researchers Qinsheng Zhang and Yongxin Chen set out to develop a fast sampling method for DMs that would require significantly fewer steps while maintaining high sample quality. To address this challenge, the researchers conducted a systematic analysis of the sampling procedure in DMs, identifying key factors that influence sample quality. Among these factors, they found that the method of discretization played a crucial role. By closely examining the learned diffusion process, Zhang and Chen proposed the . This novel approach is based on the Exponential Integrator technique designed for discretizing ordinary differential equations (ODEs) and leverages the semilinear structure of the diffusion process to reduce discretization errors. The DEIS method can be applied to any DMs and has demonstrated the capability to generate high-fidelity samples in as few as 10 steps. In experimental trials, it took approximately 3 minutes on a single A6000 GPU to produce 50k images from CIFAR10 dataset. Furthermore, by utilizing pre-trained DMs directly, Zhang and Chen achieved state-of-the-art sampling performance even when limited by the number of score function evaluations (NFE), achieving impressive results such as 3.37 FID and 9.74 Inception score with only 15 NFEs on CIFAR10. Overall, this research presents a significant advancement in fast sampling methods for , offering a practical solution for improving efficiency without compromising sample quality in generative modeling tasks.