Source separation for music is the task of isolating contributions, or stems, from different instruments recorded individually and arranged together to form a song. Such components include voice, bass, drums and any other accompaniments. Contrarily to many audio synthesis tasks where the best performances are achieved by models that directly generate the waveform, the state-of-the-art in source separation for music is to compute masks on the magnitude spectrum. In this paper, we first show that an adaptation of Conv-Tasnet (Luo & Mesgarani, 2019), a waveform-to-waveform model for source separation for speech, significantly beats the state-of-the-art on the MusDB dataset, the standard benchmark of multi-instrument source separation. Second, we observe that Conv-Tasnet follows a masking approach on the input signal, which has the potential drawback of removing parts of the relevant source without the capacity to reconstruct it. We propose Demucs, a new waveform-to-waveform model, which has an architecture closer to models for audio generation with more capacity on the decoder. Experiments on the MusDB dataset show that Demucs beats previously reported results in terms of signal to distortion ratio (SDR), but lower than Conv-Tasnet. Human evaluations show that Demucs has significantly higher quality (as assessed by mean opinion score) than Conv-Tasnet, but slightly more contamination from other sources, which explains the difference in SDR. Additional experiments with a larger dataset suggest that the gap in SDR between Demucs and Conv-Tasnet shrinks, showing that our approach is promising.