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This paper presents a neural method for distant speech recognition (DSR) that jointly separates and diarizes speech mixtures without supervision by isolated signals. A standard separation method for multi-talker DSR is a statistical multichannel method called guided source separation (GSS). While GSS does not require signal-level supervision, it relies on speaker diarization results to handle unknown numbers of active speakers. To overcome this limitation, we introduce and train a neural inference model in a weakly-supervised manner, employing the objective function of a statistical separation method. This training requires only multichannel mixtures and their temporal annotations of speaker activities. In contrast to GSS, the trained model can jointly separate and diarize speech mixtures without any auxiliary information. The experiments with the AMI corpus show that our method outperforms GSS with oracle diarization results regarding word error rates. The code is available online.