Continuous-time video frame interpolation is a fundamental technique in computer vision for its flexibility in synthesizing motion trajectories and novel video frames at arbitrary intermediate time steps. Yet, how to infer accurate intermediate motion and synthesize high-quality video frames are two critical challenges. In this paper, we present a novel VFI framework with improved treatment for these challenges. To address the former, we propose focalized trajectory fitting, which performs confidence-aware motion trajectory estimation by learning to pay focus to reliable optical flow candidates while suppressing the outliers. The second is range-nullspace synthesis, a novel frame renderer cast as solving an ill-posed problem addressed by learning decoupled components in orthogonal subspaces. The proposed framework sets new records on 7 of 10 public VFI benchmarks.