In this article, it is shown that a machine learning approach based only on data from sensors (vibration and current consumption) can be used to predict the geometric dimensioning and tolerancing quality measurement values of machined workpieces in an industrial context. First, a methodology based on a variational autoencoder approach is used, and then a metric based on the concept of Euclidean distance and the 2D latent space produced by the variational autoencoder is proposed. The proposed variational autoencoder regression model is shown capable of predicting the quality measurement values, with a mean square error of 5.2573×10−4 mm. The proposed measurement system also displays a confidence interval of ± 0.05 mm. Moreover, the resulting 2D latent space is capable of distributing and structuring data based on the quality level and of providing a quick visual support. Compared to the t-SNE method, this latent space displays a better structure. Furthermore, the proposed Euclidean distance metric is correlated to the quality level in both the predicted and observed subsets. This work is also based on an industrial dataset, thus increasing its potential for technological transfer; that in turn allows a better monitoring of the machining process, as well as the prediction of the workpiece quality.