# Tortoise and Hare Guidance: Accelerating Diffusion Model Inference with Multirate Integration

arXiv: https://arxiv.org/abs/2511.04117 · HTML: https://mlsanity.com/paper/2511.04117/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 37 of its 51 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 37)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [CogVideo: Large-scale Pretraining for Text-to-Video Generation via Transformers](https://mlsanity.com/paper/2205.15868/) (2022)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Large-scale Contrastive Language-Audio Pretraining with Feature Fusion and Keyword-to-Caption Augmentation](https://mlsanity.com/paper/2211.06687/) (2022)
- [Pseudo Numerical Methods for Diffusion Models on Manifolds](https://mlsanity.com/paper/2202.09778/) (2022)
- [Open-Sora: Democratizing Efficient Video Production for All](https://mlsanity.com/paper/2412.20404/) (2024)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [AudioLDM 2: Learning Holistic Audio Generation with Self-supervised Pretraining](https://mlsanity.com/paper/2308.05734/) (2023)
- [Rethinking FID: Towards a Better Evaluation Metric for Image Generation](https://mlsanity.com/paper/2401.09603/) (2023)
- [Applying Guidance in a Limited Interval Improves Sample and Distribution Quality in Diffusion Models](https://mlsanity.com/paper/2404.07724/) (2024)
- [MM-Diffusion: Learning Multi-Modal Diffusion Models for Joint Audio and Video Generation](https://mlsanity.com/paper/2212.09478/) (2022)
- [Delta-DiT: A Training-Free Acceleration Method Tailored for Diffusion Transformers](https://mlsanity.com/paper/2406.01125/) (2024)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [Learning-to-Cache: Accelerating Diffusion Transformer via Layer Caching](https://mlsanity.com/paper/2406.01733/) (2024)
- [MMAudio: Taming Multimodal Joint Training for High-Quality Video-to-Audio Synthesis](https://mlsanity.com/paper/2412.15322/) (2024)
- [CADS: Unleashing the Diversity of Diffusion Models through Condition-Annealed Sampling](https://mlsanity.com/paper/2310.17347/) (2023)

## Built on by (most cited first, 4 of 4)

- [Rethinking FID Through the Geometry of the Reference Dataset](https://mlsanity.com/paper/2605.29335/) (2026)
- [Understanding and Exploiting Diagonal Attention Sparsity in Autoregressive Image Generation](https://mlsanity.com/paper/2609.19702/) (2026)
- [TRAC: Trajectory-aware Reuse and Adaptive Correction for Efficient Autoregressive Video Generation](https://mlsanity.com/paper/2610.02779/) (2026)
- [What Does Fr'echet Distance Measure? A Directional Decomposition](https://mlsanity.com/paper/2610.05518/) (2026)

## Abstract (arXiv)

In this paper, we propose Tortoise and Hare Guidance (THG), a training-free strategy that accelerates diffusion sampling while maintaining high-fidelity generation. 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 (DeltaImageReward ≤ 0.032) and outperforms state-of-the-art CFG-based training-free accelerators under identical computation budgets. Our findings highlight 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.