We thank the reviewers for their appreciative and thoughtful feedback

We thank the reviewers for their appreciative and thoughtful feedback. Reviewer 1. "However, the authors fail to bring the result to their impact of the current state OT, or any novel stochastic optimization algorithm designed to compute it faster. We will further emphasize these aspects. " A measure with 0 mean. Reviewer 2. "If the paper could show the formula for that case [TV] that would be Figure 1: Large dimensions need more samples to approximate the moments of the unbalanced optimal transport plan. Reviewer 3. ""Figure 1 illustrates the convergence"... the convergence of what?" "Figure 2 is also difficult to understand.