We propose DiffSep, a new single channel source separation method based on score-matching of a stochastic differential equation (SDE). We craft a tailored continuous time diffusion-mixing process starting from the separated sources and converging to a Gaussian distribution centered on their mixture. This formulation lets us apply the machinery of score-based generative modelling. First, we train a neural network to approximate the score function of the marginal probabilities or the diffusion-mixing process. Then, we use it to solve the reverse time SDE that progressively separates the sources starting from their mixture. We propose a modified training strategy to handle model mismatch and source permutation ambiguity. Experiments on the WSJ0 2mix dataset demonstrate the potential of the method. Furthermore, the method is also suitable for speech enhancement and shows performance competitive with prior work on the VoiceBank-DEMAND dataset.