Leveraging Previous Steps: A Training-free Fast Solver for Flow Diffusion

TL;DR

This paper introduces a training-free flow-solver for flow diffusion models that leverages previous steps and polynomial interpolation to significantly reduce the number of function evaluations needed for high-quality image generation.

Contribution

The proposed flow-solver uses cached previous steps and Taylor expansion to approximate ODEs, achieving faster generation with fewer NFEs without training.

Findings

Reduces NFE while maintaining high-quality generation.

Improves FID scores significantly on multiple datasets.

Faster generation speed with minor approximation error.

Abstract

Flow diffusion models (FDMs) have recently shown potential in generation tasks due to the high generation quality. However, the current ordinary differential equation (ODE) solver for FDMs, e.g., the Euler solver, still suffers from slow generation since ODE solvers need many number function evaluations (NFE) to keep high-quality generation. In this paper, we propose a novel training-free flow-solver to reduce NFE while maintaining high-quality generation. The key insight for the flow-solver is to leverage the previous steps to reduce the NFE, where a cache is created to reuse these results from the previous steps. Specifically, the Taylor expansion is first used to approximate the ODE. To calculate the high-order derivatives of Taylor expansion, the flow-solver proposes to use the previous steps and a polynomial interpolation to approximate it, where the number of orders we could approximate equals the number of previous steps we cached. We also prove that the flow-solver has a more minor approximation error and faster generation speed. Experimental results on the CIFAR-10, CelebA-HQ, LSUN-Bedroom, LSUN-Church, ImageNet, and real text-to-image generation prove the efficiency of the flow-solver. Specifically, the flow-solver improves the FID-30K from 13.79 to 6.75, from 46.64 to 19.49 with $\text{NFE}=10$ on CIFAR-10 and LSUN-Church, respectively.