Neural priors are a promising direction to capture low-level vision statistics without relying on handcrafted regularizers. Recent works have successfully shown the use of neural architecture biases to implicitly regularize image denoising, super-resolution, inpainting, synthesis, scene flow, among others. They do not rely on large-scale datasets to capture prior statistics and thus generalize well to out-of-the-distribution data. Inspired by such advances, we investigate neural priors for trajectory representation. Traditionally, trajectories have been represented by a set of handcrafted bases that have limited expressibility. Here, we propose a neural trajectory prior to capture continuous spatio-temporal information without the need for offline data. We demonstrate how our proposed objective is optimized during runtime to estimate trajectories for two important tasks—Non-Rigid Structure from Motion (NRSfM) and lidar scene flow integration for self-driving scenes. Our results are competitive to many state-of-the-art methods for both tasks.