Multi-fidelity fusion has become an important surrogate technique, which provides insights into expensive computer simulations and effectively improves decision-making, e.g., optimization, with less computational cost. Multi-fidelity fusion is much more computationally efficient compared to traditional single-fidelity surrogates. Despite the fast advancement of multi-fidelity fusion techniques, they lack a systematic framework to make use of the fidelity indicator, deal with high-dimensional and arbitrary data structure, and scale well to infinite-fidelity problems. In this work, we first generalize the popular autoregression (AR) to derive a novel linear fidelity differential equation (FiDE), paving the way to tractable infinite-fidelity fusion. We generalize FiDE to a high-dimensional system, which also provides a unifying framework to seemly bridge the gap between many multi- and single-fidelity GP-based models. We then propose ContinuAR, a rank-1 approximation solution to FiDEs, which is tractable to train, compatible with arbitrary multi-fidelity data structure, linearly scalable to the output dimension, and most importantly, delivers consistent SOTA performance with a significant margin over the baseline methods. Compared to the SOTA infinite-fidelity fusion, IFC, ContinuAR achieves up to 4x improvement in accuracy and 62,500x speedup in training time.