  This article demonstrates that flexible and statistically tractable
multi-modal diffusion models can be attained by transformation of simple
well-known diffusion models such as the Ornstein-Uhlenbeck model, or more
generally a Pearson diffusion. The transformed diffusion inherits many
properties of the underlying simple diffusion including its mixing rates and
distributions of first passage times. Likelihood inference and martingale
estimating functions are considered in the case of a discretely observed
bimodal diffusion. It is further demonstrated that model parameters can be
identified and estimated when the diffusion is observed with additional
measurement error. The new approach is applied to molecular dynamics data in
form of a reaction coordinate of the small Trp-zipper protein, for which the
folding and unfolding rates are estimated. The new models provide a better fit
to this type of protein folding data than previous models because the diffusion
coefficient is state-dependent.
