Diffusion Transformers (DiTs) have demonstrated exceptional performance in high-fidelity image and video generation. To reduce their substantial computational costs, feature caching techniques have been proposed to accelerate inference by reusing hidden representations from previous timesteps. However, current methods often struggle to maintain generation quality at high acceleration ratios, where prediction errors increase sharply due to the inherent instability of long-step forecasting. In this work, we adopt an ordinary differential equation (ODE) perspective on the hidden-feature sequence, modeling layer representations along the trajectory as a feature-ODE. We attribute the degradation of existing caching strategies to their inability to robustly integrate historical features under large skipping intervals. To address this, we propose FoCa (Forecast-then-Calibrate), which treats feature caching as a feature-ODE solving problem. Extensive experiments on image, video generation, and super-resolution tasks demonstrate the effectiveness of FoCa, especially under aggressive acceleration. Without additional training, FoCa achieves near-lossless speedups of 5.50× on FLUX, 6.45× on HunyuanVideo, 3.17× on Inf-DiT, and maintains high quality with a 4.53× speedup on DiT.