# ETC: training-free diffusion models acceleration with Error-aware Trend Consistency

arXiv: https://arxiv.org/abs/2510.24129 · HTML: https://mlsanity.com/paper/2510.24129/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 34 of its 38 references that are in the map.
- First posted on arXiv 28 Oct 2025.

## Placed in

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

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [VBench: Comprehensive Benchmark Suite for Video Generative Models](https://mlsanity.com/paper/2311.17982/) (2023)
- [Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2304.08818/) (2023)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Large-scale Contrastive Language-Audio Pretraining with Feature Fusion and Keyword-to-Caption Augmentation](https://mlsanity.com/paper/2211.06687/) (2022)
- [Open-Sora: Democratizing Efficient Video Production for All](https://mlsanity.com/paper/2412.20404/) (2024)
- [Simple and Controllable Music Generation](https://mlsanity.com/paper/2306.05284/) (2023)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [Timestep Embedding Tells: It's Time to Cache for Video Diffusion Model](https://mlsanity.com/paper/2411.19108/) (2024)
- [Efficient Training of Audio Transformers with Patchout](https://mlsanity.com/paper/2110.05069/) (2021)
- [Fr'echet Audio Distance: A Metric for Evaluating Music Enhancement Algorithms](https://mlsanity.com/paper/1812.08466/) (2018)
- [Does Knowledge Distillation Really Work?](https://mlsanity.com/paper/2106.05945/) (2021)
- [Delta-DiT: A Training-Free Acceleration Method Tailored for Diffusion Transformers](https://mlsanity.com/paper/2406.01125/) (2024)
- [Learning-to-Cache: Accelerating Diffusion Transformer via Layer Caching](https://mlsanity.com/paper/2406.01733/) (2024)
- [TangoFlux: Super Fast and Faithful Text to Audio Generation with Flow Matching and Clap-Ranked Preference Optimization](https://mlsanity.com/paper/2412.21037/) (2024)

## Abstract (arXiv)

Diffusion models have achieved remarkable generative quality but remain bottlenecked by costly iterative sampling. Recent training-free methods accelerate diffusion process by reusing model outputs. However, these methods ignore denoising trends and lack error control for model-specific tolerance, leading to trajectory deviations under multi-step reuse and exacerbating inconsistencies in the generated results. To address these issues, we introduce Error-aware Trend Consistency (ETC), a framework that (1) introduces a consistent trend predictor that leverages the smooth continuity of diffusion trajectories, projecting historical denoising patterns into stable future directions and progressively distributing them across multiple approximation steps to achieve acceleration without deviating; (2) proposes a model-specific error tolerance search mechanism that derives corrective thresholds by identifying transition points from volatile semantic planning to stable quality refinement. Experiments show that ETC achieves a 2.65x acceleration over FLUX with negligible (-0.074 SSIM score) degradation of consistency.