Non-Intrusive Load Monitoring (NILM) seeks to save energy by estimating individual appliance power usage from a single aggregate measurement. Deep neural networks have become increasingly popular in attempting to solve NILM problems. However most used models are used for Load Identification rather than online Source Separation. Among source separation models, most use a single-task learning approach in which a neural network is trained exclusively for each appliance. This strategy is computationally expensive and ignores the fact that multiple appliances can be active simultaneously and dependencies between them. The rest of models are not causal, which is important for real-time application. Inspired by Convtas-Net, a model for speech separation, we propose Conv-NILM-net, a fully convolutional framework for end-to-end NILM. Conv-NILM-net is a causal model for multi appliance source separation. Our model is tested on two real datasets REDD and UK-DALE and clearly outperforms the state of the art while keeping a significantly smaller size than the competing models.