This paper presents a deep regression model to estimation of the weld bead parameters in welding tasks. It is an aggregate of deep regression blocks where number of these blocks is proportional to the cardinality of the weld parameters. These blocks are trained simultaneously and share an identical structure with four-hidden-layer Sigmoid activation functions and a linear transformation at their outputs. Moreover, they incorporate a new meta-parameter, shared by all the hidden layers of a given block, to maintain the quality of the gradients of their respective weight matrices. This allows the model to further reduce the deviation of its estimates from the expected values of the weld parameters to significantly minimize its estimation error. The evaluation of the performance of this approach in contrast to state-of-the-art techniques in the literature shows a significant improvement in estimating these values for different welding processes. Furthermore, the proposed deep regression network is capable of retaining its performance when presented with combined data of different welding techniques. This is a nontrivial result in attaining an scalable model whose quality of estimation is independent of adopted welding techniques.