Continuous time series data often comprise or contain repeated motifs — patterns that have similar shape, and yet exhibit nontrivial variability. Identifying these motifs, even in the presence of variation, is an important subtask in both unsupervised knowledge discovery and constructing useful features for discriminative tasks. This paper addresses this task using a probabilistic framework that models generation of data as switching between a random walk state and states that generate motifs. A motif is generated from a continuous shape template that can undergo non-linear transformations such as temporal warping and additive noise. We propose an unsupervised algorithm that simultaneously discovers both the set of canonical shape templates and a template-specific model of variability manifested in the data. Experimental results on three real-world data sets demonstrate that our model is able to recover templates in data where repeated instances show large variability. The recovered templates provide higher classification accuracy and coverage when compared to those from alternatives such as random projection based methods and simpler generative models that do not model variability. Moreover, in analyzing physiological signals from infants in the ICU, we discover both known signatures as well as novel physiomarkers.