Accurate prediction of the electricity-load profile is at the base of the optimal use of renewable energies and of diminishing carbon footprint. In practice, electricity suppliers are required to commit in advance to a certain load profile and any discrepancy from it must be compensated, a priori, via non-renewable energies. We propose a nonparametric approach based on Stochastic Differential Equations (SDEs) to generate probabilistic forecasts for the day-ahead electricity consumption of an agglomerate of buildings in the city of Lausanne (Switzerland). The trend of the profile is given by a deterministic model, while the fluctuations around it are introduced with a Brownian noise, whose related process reverts to its mean. The inference of the parameters of the deterministic model and of the SDE is carried out by maximizing the likelihood of the process given by Girsanov’s theorem. On one hand, we show that the pointwise prediction of the consumption is reliable and close to the real trend, on the other hand, we provide sharp confidence bands capturing the probability distribution of the data. Finally, we compare our model with a Deep-Learning forecaster built upon Quantile Recurrent Neural Network (QRNN). We highlight the main differences between the two approaches, showing that both lead to satisfactory conclusions.