Event cameras, with their high temporal resolution, dynamic range, and low power consumption, are particularly good at time-sensitive applications like deblurring and frame interpolation. However, their performance is hindered by latency variability, especially under low-light conditions and with fast-moving objects. This paper addresses the challenge of latency in event cameras — the temporal discrepancy between the actual occurrence of changes in the corresponding timestamp assigned by the sensor. Focusing on event-guided deblurring and frame interpolation tasks, we propose a latency correction method based on a parameterized latency model. To enable data-driven learning, we develop an event-based temporal fidelity to describe the sharpness of latent images reconstructed from events and the corresponding blurry images, and reformulate the event-based double integral model differentiable to latency. The proposed method is validated using synthetic and real-world datasets, demonstrating the benefits of latency correction for deblurring and interpolation across different lighting conditions.