Ischemic stroke volume is a strong predictor of functional outcome and may play a role in decision making of reperfusion therapy in the late time window (< 6hr of stroke onset to MRI time) when it is obtained along with penumbra volume. Automatic diffusion lesion segmentation can be performed using a commercial software package and is typically based on a fixed apparent diffusion coefficient (ADC) threshold. ADC values alone may not be guaranteed to be highly accurate in the identification of diffusion lesions. Deep learning has the potential to improve the accuracy of diffusion lesion segmentation, provided that a large set of correctly labeled lesion mask data is used for training. The purpose of this study is to evaluate deep learning-based segmentation methods and compare them with three fixed ADC threshold-based methods. U-net was adopted to train a segmentation model. Two U-net models were developed: a model "U-net (DWI+ADC)" trained from DWI and ADC data, and a model "U-net (DWI)" trained from DWI data only. 296 subjects were used for training, and 134 subjects were used for testing. An expert neurologist manually delineated infarct masks on DWI, which served as ground-truth reference. Lesion volume measurements from the two U-net methods and three fixed ADC threshold-based methods were compared against lesion volume measurements from manual segmentation. In testing, the "U-net (DWI+ADC)" method outperformed other methods in lesion volume measurement, with the smallest root-mean-square error of 2.96 ml and the highest Pearson correlation coefficient of 0.997. The proposed method has the potential to automatically measure diffusion lesion volume in a fast and accurate manner, in patients with acute ischemic stroke.