We propose mixture to mixture (M2M) training, a weakly-supervised neural speech separation algorithm that leverages close-talk mixtures as a weak supervision for training discriminative models to separate far-field mixtures. Our idea is that, for a target speaker, its close-talk mixture has a much higher signal-to-noise ratio (SNR) of the target speaker than any far-field mixtures, and hence could be utilized to design a weak supervision for separation. To realize this, at each training step we feed a far-field mixture to a deep neural network (DNN) to produce an intermediate estimate for each speaker, and, for each of considered close-talk and far-field microphones, we linearly filter the DNN estimates and optimize a loss so that the filtered estimates of all the speakers can sum up to the mixture captured by each of the considered microphones. Evaluation results on a 2-speaker separation task in simulated reverberant conditions show that M2M can effectively leverage close-talk mixtures as a weak supervision for separating far-field mixtures.