Deep Learning neural networks are powerful tools to capture information from input data, and have been increasingly applied in astrophysical studies. However, without proper treatments, data-driven algorithms such as neural networks are prone to overfitting on information that is correlated yet not causally related to certain tasks (e.g., systematics, the prior distribution of training data, etc.), and thus result in a biased output harmful for subsequent analyses. It is therefore essential to correct biases caused by such irrelevant information. Using galaxy photometric redshift estimation as an example, I will demonstrate the approaches that we exploit to tackle the two major forms of biases in the existing Deep Learning techniques, namely the redshift-dependent residual and the mode collapse. Experiments show that these approaches are effective and potentially useful in real astrophysical analyses. They are also meaningful in helping us understand the training of neural networks for general classification or regression problems in computer science applications.