# TC-Pad'e: Trajectory-Consistent Pad'e Approximation for Diffusion Acceleration

arXiv: https://arxiv.org/abs/2603.02943 · HTML: https://mlsanity.com/paper/2603.02943/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 51 of its 64 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Placed in

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

## Builds on (most cited first, 30 of 51)

- [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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [HunyuanVideo: A Systematic Framework For Large Video Generative Models](https://mlsanity.com/paper/2412.03603/) (2024)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Autoregressive Model Beats Diffusion: Llama for Scalable Image Generation](https://mlsanity.com/paper/2406.06525/) (2024)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [DeepCache: Accelerating Diffusion Models for Free](https://mlsanity.com/paper/2312.00858/) (2023)
- [VBench-2.0: Advancing Video Generation Benchmark Suite for Intrinsic Faithfulness](https://mlsanity.com/paper/2503.21755/) (2025)
- [Fast High-Resolution Image Synthesis with Latent Adversarial Diffusion Distillation](https://mlsanity.com/paper/2403.12015/) (2024)
- [Q-Diffusion: Quantizing Diffusion Models](https://mlsanity.com/paper/2302.04304/) (2023)
- [Timestep Embedding Tells: It's Time to Cache for Video Diffusion Model](https://mlsanity.com/paper/2411.19108/) (2024)
- [Post-training Quantization on Diffusion Models](https://mlsanity.com/paper/2211.15736/) (2022)
- [Delta-DiT: A Training-Free Acceleration Method Tailored for Diffusion Transformers](https://mlsanity.com/paper/2406.01125/) (2024)
- [Accelerating Diffusion Transformers with Token-wise Feature Caching](https://mlsanity.com/paper/2410.05317/) (2024)
- [Cache Me if You Can: Accelerating Diffusion Models through Block Caching](https://mlsanity.com/paper/2312.03209/) (2023)
- [Real-Time Video Generation with Pyramid Attention Broadcast](https://mlsanity.com/paper/2408.12588/) (2024)

## Built on by (most cited first, 10 of 10)

- [simpleposter: A simple baseline for product poster generation](https://mlsanity.com/paper/2605.08784/) (2026)
- [JND-Guided Neural Watermarking with Spatial Transformer Decoding for Screen-Capture Robustness](https://mlsanity.com/paper/2603.26766/) (2026)
- [Transmittance-Guided Structure-Texture Decomposition for Nighttime Image Dehazing](https://mlsanity.com/paper/2603.29507/) (2026)
- [Hierarchical Awareness Adapters with Hybrid Pyramid Feature Fusion for Dense Depth Prediction](https://mlsanity.com/paper/2604.03339/) (2026)
- [Do You Need Text Rectification? Soft Attention Mask Embedding for Rectification-Free Scene Text Spotting](https://mlsanity.com/paper/2605.18173/) (2026)
- [Yuvion VL: A Multimodal Foundation Model for Adversarial Content and AI Safety](https://mlsanity.com/paper/2606.25034/) (2026)
- [Fully Unleashing the Multimodal Attacker: Meta-Adaptive Jailbreaking of Vision-Language Models](https://mlsanity.com/paper/2608.27531/) (2026)
- [EvoHarmBench: Breaking Content Moderation with Iterative Human-Like Evasion](https://mlsanity.com/paper/2608.27844/) (2026)
- [Contour-Guided Spectral Routing for Robust Real-Time Pedestrian Detection](https://mlsanity.com/paper/2609.14383/) (2026)
- [Hybrid-Basis Feature Forecasting for Diffusion Sampling Acceleration](https://mlsanity.com/paper/2610.05254/) (2026)

## Abstract (arXiv)

Despite achieving state-of-the-art generation quality, diffusion models are hindered by the substantial computational burden of their iterative sampling process. While feature caching techniques achieve effective acceleration at higher step counts (e.g., 50 steps), they exhibit critical limitations in the practical low-step regime of 20-30 steps. As the interval between steps increases, polynomial-based extrapolators like TaylorSeer suffer from error accumulation and trajectory drift. Meanwhile, conventional caching strategies often overlook the distinct dynamical properties of different denoising phases. To address these challenges, we propose Trajectory-Consistent Pad'e approximation, a feature prediction framework grounded in Pad'e approximation. By modeling feature evolution through rational functions, our approach captures asymptotic and transitional behaviors more accurately than Taylor-based methods. To enable stable and trajectory-consistent sampling under reduced step counts, TC-Pad'e incorporates (1) adaptive coefficient modulation that leverages historical cached residuals to detect subtle trajectory transitions, and (2) step-aware prediction strategies tailored to the distinct dynamics of early, mid, and late sampling stages. Extensive experiments on DiT-XL/2, FLUX.1-dev, and Wan2.1 across both image and video generation demonstrate the effectiveness of TC-Pad'e. For instance, TC-Pad'e achieves 2.88x acceleration on FLUX.1-dev and 1.72x on Wan2.1 while maintaining high quality across FID, CLIP, Aesthetic, and VBench-2.0 metrics, substantially outperforming existing feature caching methods.