Interstitial lung diseases (ILDs) are adverse disorders, damaging the lung tissues, thus making timely diagnosis imperative. To counter the scarcity of publicly available high-resolution computed tomography (HRCT) data, architecture employing HRCT and x-ray data have been proposed for diagnosing ILDs. A model is first trained to diagnose three ILDs and a healthy lung from x-ray data and then with a small amount of HRCT data of the same four classes. We introduce an EfficientNet+AlexNet model and a custom deep convolutional neural network and compare their performances with different weight initialization at the start of x-ray image training. The EfficientNet+AlexNet model initialized with ImageNet weights performed best on the x-ray dataset and was later used for domain adaptation. We also compare our model's performance to a single pre-trained EfficientNetB0 model (trained on the same HRCT data). Our model gave an accuracy of 97.4% on the testing dataset, a notable increase in the performance compared to the recently proposed methodologies. The experimental results and graphical plots depict the superiority of domain adaptation and the potentials of weights that are a starting point for training the models.