Accurate quantification of cardiac valve regurgitation jets is fundamental for guiding treatment. Cardiac ultrasound is the preferred diagnostic tool, but current methods for measuring the regurgitant volume (RVol) are limited by low accuracy and high interobserver variability. Following recent research, quantitative estimators of orifice size and RVol based on high frame rate 3-D ultrasound have been proposed, but measurement accuracy is limited by the wide point spread function (PSF) relative to the orifice size. The aim of this article was to investigate the use of deep learning to estimate both the orifice size and the RVol. A simulation model was developed to simulate the power-Doppler images of blood flow through orifices with different geometries. A convolutional neural network (CNN) was trained on 30 000 image pairs. The network was used to reconstruct orifices from power-Doppler data, which facilitated estimators for regurgitant orifice areas and flow volumes. We demonstrate that the network improves orifice shape reconstruction, as well as the accuracy of orifice area and flow volume estimation, compared with a previous approach based on thresholding of the power-Doppler signal (THD), and compared with spatially invariant deconvolution (DC). Our approach reduces the area estimation error on simulations: (THD: 13.2 ± 9.9 mm2, DC: 12.8 ± 15.8 mm2, and ours: 3.5 ± 3.2 mm2). In a phantom experiment, our approach reduces both area estimation error (THD: 10.4 ± 8.4 mm2, DC: 10.98 ± 8.17, and ours: 9.9 ± 6.0 mm2) and flow rate estimation error (THD: 20.3 ± 9.9 ml/s, DC: 18.14 ± 13.01 ml/s, and ours: 7.1 ± 10.6 ml/s). We also demonstrate in vivo feasibility for six patients with aortic insufficiency, compared with standard echocardiography and magnetic resonance references.