We consider the problem of acoustic modeling of noisy speech data, where the uncertainty over the data is given by a Gaussian distribution. While this uncertainty has been exploited at the decoding stage via uncertainty decoding, its usage at the training stage remains limited to static model adaptation. We introduce a new Expectation Maximisation (EM) based technique, which we call uncertainty training, that allows us to train Gaussian mixture models (GMMs) or hidden Markov models (HMMs) directly from noisy data with dynamic uncertainty. We evaluate the potential of this technique for a GMM-based speaker recognition task on speech data corrupted by real-world domestic background noise, using a state-of-the-art signal enhancement technique and various uncertainty estimation techniques as a front-end. Compared to conventional training, the proposed training algorithm results in 1% to 2% absolute improvement in speaker recognition accuracy by training from either matched, unmatched or multi-condition noisy data. This algorithm is also applicable with minor modifications to maximum a posteriori (MAP) or maximum likelihood linear regression (MLLR) acoustic model adaptation from noisy data and to other data than audio.