Lab values and biomarkers are often irregularly and asynchronously measured, making them difficult to use in predictive modeling. However, temporal trends can still be recovered from these measurements and are important for predicting disease onsets. We'll present a novel model of high-dimensional temporal input and high-dimensional output. Our model is composed of two convolutional neural network components. The first component is an efficient convolution-based formulation of multivariate kernel regression, which allows us to estimate each biomarker at each time point from the rest of the biomarker time series. The second component is a multi-resolution, multi-task convolutional neural network that recovers temporal trends most predictive of up to 170 diseases. We'll show how this multi-task formulation allows us to retain the correlation structure among the diseases throughout the training. Our experiments on data from 298K individuals over 8 years, up to 100 common lab measurements, and 171 diseases show that the temporal signatures learned via convolution are significantly more predictive than baselines commonly used for early disease diagnosis.