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

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.