NeurIPS 2025

Tortoise and Hare Guidance: Accelerating Diffusion
Model Inference with Multirate Integration
Yunghee Lee
Byeonghyun Pak
Junwha Hong
Hoseong Kim†
Agency for Defense Development
{yhl, byeonghyun_pak, qbit, hoseongkim}@add.re.kr
Abstract
In this paper, we propose Tortoise and Hare Guidance (THG), a training-free
strategy that accelerates diffusion sampling while maintaining high-fidelity gen-
eration. We demonstrate that the noise estimate and the additional guidance
term exhibit markedly different sensitivity to numerical error by reformulating
the classifier-free guidance (CFG) ODE as a multirate system of ODEs. Our
error-bound analysis shows that the additional guidance branch is more robust to
approximation, revealing substantial redundancy that conventional solvers fail to
exploit. Building on this insight, THG significantly reduces the computation of the
additional guidance: the noise estimate is integrated with the tortoise equation on
the original, fine-grained timestep grid, while the additional guidance is integrated
with the hare equation only on a coarse grid. We also introduce (i) an error-bound-
aware timestep sampler that adaptively selects step sizes and (ii) a guidance-scale
scheduler that stabilizes large extrapolation spans. THG reduces the number of
function evaluations (NFE) by up to 30% with virtually no loss in generation
fidelity (∆ImageReward ≤0.032) and outperforms state-of-the-art CFG-based
training-free accelerators under identical computation budgets. Our findings high-
light the potential of multirate formulations for diffusion solvers, paving the way for
real-time high-quality image synthesis without any model retraining. The source
code is available at https://github.com/yhlee-add/THG.
1
Introduction
Diffusion models (DMs) have become the state-of-the-art generative model for images [10, 40, 47]
and, more recently, for video [20, 1, 52, 21] and audio-visual content [5, 41]. Despite their impressive
quality, sampling is costly: each outp...