  Joint pedestrian trajectory prediction has long grappled with the inherent
unpredictability of human behaviors. Recent investigations employing variants
of conditional diffusion models in trajectory prediction have exhibited notable
success. Nevertheless, the heavy dependence on accurate historical data results
in their vulnerability to noise disturbances and data incompleteness. To
improve the robustness and reliability, we introduce the Guided Full Trajectory
Diffuser (GFTD), a novel diffusion model framework that captures the joint full
(historical and future) trajectory distribution. By learning from the full
trajectory, GFTD can recover the noisy and missing data, hence improving the
robustness. In addition, GFTD can adapt to data imperfections without
additional training requirements, leveraging posterior sampling for reliable
prediction and controllable generation. Our approach not only simplifies the
prediction process but also enhances generalizability in scenarios with noise
and incomplete inputs. Through rigorous experimental evaluation, GFTD exhibits
superior performance in both trajectory prediction and controllable generation.
