Accurate pedestrian trajectory prediction is crucial for ensuring safety and efficiency in autonomous driving and human-robot interaction scenarios. Earlier studies primarily utilized sufficient observational data to predict future trajectories. However, in real-world scenarios, such as pedestrians suddenly emerging from blind spots, sufficient observational data is often unavailable (i.e. momentary trajectory), making accurate prediction challenging and increasing the risk of traffic accidents. Therefore, advancing research on pedestrian trajectory prediction under extreme scenarios is critical for enhancing traffic safety. In this work, we propose a novel framework termed Diffusion^2, tailored for momentary trajectory prediction. Diffusion^2 consists of two sequentially connected diffusion models: one for backward prediction, which generates unobserved historical trajectories, and the other for forward prediction, which forecasts future trajectories. Given that the generated unobserved historical trajectories may introduce additional noise, we propose a dual-head parameterization mechanism to estimate their aleatoric uncertainty and design a temporally adaptive noise module that dynamically modulates the noise scale in the forward diffusion process. Empirically, Diffusion^2 sets a new state-of-the-art in momentary trajectory prediction on ETH/UCY and Stanford Drone datasets.