We introduce a robust probabilistic approach to modeling shape contours based on a low-dimensional, nonlinear latent variable model. In contrast to existing techniques that use objective functions in data space without explicit noise models, we are able to extract complex shape variation from noisy data. Most approaches to learning shape models slide observed data points around fixed contours and hence, require a correctly labeled 'reference shape' to prevent degenerate solutions. In our method, unobserved curves are reparameterized to explain the fixed data points, so this problem does not arise. The proposed algorithms are suitable for use with arbitrary basis functions and are applicable to both open and closed shapes; their effectiveness is demonstrated through illustrative examples, quantitative assessment on benchmark data sets and a visualization task.