Quasi-Taylor Samplers for Diffusion Generative Models based on Ideal Derivatives

TL;DR

This paper introduces efficient quasi-Taylor samplers for diffusion models that reduce neural function evaluations by using ideal derivatives and a single point approximation, achieving comparable or better image synthesis quality.

Contribution

The paper presents a novel sampling method based on Taylor expansion with ideal derivatives, improving efficiency in diffusion models by reducing NFEs.

Findings

Achieved high-quality image synthesis with fewer NFEs.

Outperformed or matched DDIM and Runge-Kutta methods.

Validated the approach through experimental results.

Abstract

Diffusion generative models have emerged as a new challenger to popular deep neural generative models such as GANs, but have the drawback that they often require a huge number of neural function evaluations (NFEs) during synthesis unless some sophisticated sampling strategies are employed. This paper proposes new efficient samplers based on the numerical schemes derived by the familiar Taylor expansion, which directly solves the ODE/SDE of interest. In general, it is not easy to compute the derivatives that are required in higher-order Taylor schemes, but in the case of diffusion models, this difficulty is alleviated by the trick that the authors call ``ideal derivative substitution,'' in which the higher-order derivatives are replaced by tractable ones. To derive ideal derivatives, the authors argue the ``single point approximation,'' in which the true score function is approximated by a conditional one, holds in many cases, and considered the derivatives of this approximation. Applying thus obtained new quasi-Taylor samplers to image generation tasks, the authors experimentally confirmed that the proposed samplers could synthesize plausible images in small number of NFEs, and that the performance was better or at the same level as DDIM and Runge-Kutta methods. The paper also argues the relevance of the proposed samplers to the existing ones mentioned above.