Fast Sampling of Diffusion Models via Operator Learning (2211.13449v3)

Abstract: Diffusion models have found widespread adoption in various areas. However, their sampling process is slow because it requires hundreds to thousands of network evaluations to emulate a continuous process defined by differential equations. In this work, we use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose a parallel decoding method that generates images with only one model forward pass. We propose diffusion model sampling with neural operator (DSNO) that maps the initial condition, i.e., Gaussian distribution, to the continuous-time solution trajectory of the reverse diffusion process. To model the temporal correlations along the trajectory, we introduce temporal convolution layers that are parameterized in the Fourier space into the given diffusion model backbone. We show our method achieves state-of-the-art FID of 3.78 for CIFAR-10 and 7.83 for ImageNet-64 in the one-model-evaluation setting.

• The paper introduces DSNO, a novel diffusion sampling method that enables parallel decoding in a single forward pass.
• It leverages Fourier neural operators and temporal convolution blocks to efficiently model probability flows with minimal model overhead.
• Experimental results report FID scores of 3.78 on CIFAR-10 and 7.83 on ImageNet-64, underscoring its practical real-time applications.

Fast Sampling of Diffusion Models via Operator Learning

The paper "Fast Sampling of Diffusion Models via Operator Learning" primarily addresses the slow sampling process inherent in diffusion models, proposing a novel approach using neural operators to significantly accelerate this process. Diffusion models have demonstrated efficacy across various domains, but their computational demands have rendered them less suitable for time-sensitive applications. The authors propose a method called Diffusion Model Sampling with Neural Operator (DSNO), which utilizes neural operators to advance the sampling speed without the sequential limitations of traditional methods. This paper's contributions are pertinent to experienced researchers engaged in designing efficient generative models.

Key Contributions

1. Parallel Decoding: A cornerstone of the paper is the introduction of a parallel decoding method. Unlike existing methods that rely on sequential processing, DSNO enables the prediction of probability flow trajectories in a single forward pass, demonstrating significant improvement in computational efficiency.
2. Neural Operator Integration: The paper leverages Fourier neural operators, recognized for their capabilities in solving differential equations efficiently, integrating them with existing diffusion model architectures to provide discretization invariant and universal approximation properties.
3. Temporal Convolution Blocks: Parameterized in Fourier space, these blocks model trajectories more effectively than traditional numerical solvers. They seamlessly fit within the neural architecture, contributing to only a marginal increase in model size, yet they bring substantial enhancement in sampling speed.
4. Strong Numerical Results: DSNO achieves a state-of-the-art Fréchet Inception Distance (FID) score of 3.78 on CIFAR-10 and 7.83 on ImageNet-64 with only one model evaluation. This performance underscores the potential for real-time applications where traditional diffusion models would be impractical due to latency.

Implications and Speculations

The implications of this research are both practical and theoretical. Practically, the approach presents a means to deploy diffusion models in applications like AI-assisted art and design or decision-making systems that demand rapid feedback and autonomous generation. Theoretically, integrating neural operators with generative diffusion models may inspire further exploration into their applicability to other continuous processes and trajectory-sampling problems.

From a speculative standpoint, the paper hints at future developments including potential extensions to guided sampling and transformer-based architectures, which would further enhance the flexibility and applicability of DSNO. Additionally, the temporal continuity offered by DSNO opens avenues for applications necessitating back-and-forth sampling over time, such as in adversarial purification.

Conclusion

The paper represents a significant step forward in addressing the computational inefficiencies of diffusion models. By innovatively applying neural operators and introducing parallel processing within this framework, the authors provide an enhanced method for high-quality, rapid sampling of generative models. As diffusion models continue to see increased adoption across sectors demanding efficient computation, approaches like DSNO could play a critical role in shaping future developments in the field.