  Forecasting complex vehicle and pedestrian multi-modal distributions requires
powerful probabilistic approaches. Normalizing flows (NF) have recently emerged
as an attractive tool to model such distributions. However, a key drawback is
that independent samples drawn from a flow model often do not adequately
capture all the modes in the underlying distribution. We propose
Likelihood-Based Diverse Sampling (LDS), a method for improving the quality and
the diversity of trajectory samples from a pre-trained flow model. Rather than
producing individual samples, LDS produces a set of trajectories in one shot.
Given a pre-trained forecasting flow model, we train LDS using gradients from
the model, to optimize an objective function that rewards high likelihood for
individual trajectories in the predicted set, together with high spatial
separation among trajectories. LDS outperforms state-of-art post-hoc neural
diverse forecasting methods for various pre-trained flow models as well as
conditional variational autoencoder (CVAE) models. Crucially, it can also be
used for transductive trajectory forecasting, where the diverse forecasts are
trained on-the-fly on unlabeled test examples. LDS is easy to implement, and we
show that it offers a simple plug-in improvement over baselines on two
challenging benchmarks. Code is at: https://github.com/JasonMa2016/LDS
