  The ability to forecast a set of likely yet diverse possible future behaviors
of an agent (e.g., future trajectories of a pedestrian) is essential for
safety-critical perception systems (e.g., autonomous vehicles). In particular,
a set of possible future behaviors generated by the system must be diverse to
account for all possible outcomes in order to take necessary safety
precautions. It is not sufficient to maintain a set of the most likely future
outcomes because the set may only contain perturbations of a single outcome.
While generative models such as variational autoencoders (VAEs) have been shown
to be a powerful tool for learning a distribution over future trajectories,
randomly drawn samples from the learned implicit likelihood model may not be
diverse -- the likelihood model is derived from the training data distribution
and the samples will concentrate around the major mode that has most data. In
this work, we propose to learn a diversity sampling function (DSF) that
generates a diverse and likely set of future trajectories. The DSF maps
forecasting context features to a set of latent codes which can be decoded by a
generative model (e.g., VAE) into a set of diverse trajectory samples.
Concretely, the process of identifying the diverse set of samples is posed as a
parameter estimation of the DSF. To learn the parameters of the DSF, the
diversity of the trajectory samples is evaluated by a diversity loss based on a
determinantal point process (DPP). Gradient descent is performed over the DSF
parameters, which in turn move the latent codes of the sample set to find an
optimal diverse and likely set of trajectories. Our method is a novel
application of DPPs to optimize a set of items (trajectories) in continuous
space. We demonstrate the diversity of the trajectories produced by our
approach on both low-dimensional 2D trajectory data and high-dimensional human
motion data.
