  Ambiguity is ubiquitous in human communication. Previous approaches in
Human-Robot Interaction (HRI) have often relied on predefined interaction
templates, leading to reduced performance in realistic and open-ended
scenarios. To address these issues, we present a large-scale dataset, \invig,
for interactive visual grounding under language ambiguity. Our dataset
comprises over 520K images accompanied by open-ended goal-oriented
disambiguation dialogues, encompassing millions of object instances and
corresponding question-answer pairs. Leveraging the \invig dataset, we conduct
extensive studies and propose a set of baseline solutions for end-to-end
interactive visual disambiguation and grounding, achieving a 45.6\% success
rate during validation. To the best of our knowledge, the \invig dataset is the
first large-scale dataset for resolving open-ended interactive visual
grounding, presenting a practical yet highly challenging benchmark for
ambiguity-aware HRI. Codes and datasets are available at:
\href{https://openivg.github.io}{https://openivg.github.io}.
